Well, I'm about to do a lot of agreeing and disagreeing with you. So before I get to all of that, I wanted to genuinely say thanks for writing me that essay. This may surprise you, but it's pretty rare for anyone to listen to my inane Fallout ramblings. Much less fire back with as much obvious passion on the subject.
That being said, allow me to respond in kind.
I flat out agree with your assessment of the combat in 4. The RPG elements grind against the action oriented combat, and both are made worse for it. Though when the numbers come out right, I stand by 4 having the highest combat ''fun ceiling'' of the series due to the vastly improved combat mechanics. Even if it has the lowest floor as well due to the poor interplay with the RPG elements. If you were to remove the Leveling and Enemy scaling from these games, there is no doubt which one would be the most fun to play.
Also you may be overselling the need to strategize in 3/NV. Even on Very Hard, it's never been... difficult. With the abundance of aid items and no penalty to using them, to the abuse-ability of VATS, to the broken items and perks, you are basically never going to need to strategize. (Speaking of unarmed runs, is ''Super Slam'' a strategy?)
As far as Exploration, your points on NV I mostly agree with. Though to say you ''find nothing'' while exploring is an overstatement. I stumbled on Vault 11 by just exploring for example. Just look at NV's map and you'll see that any direction you head will take you to a very interesting location with a great story attached. I'd argue the problem with NV's exploration isn't the destination, but the journey. The game usually railroads players to where it wants you to go. Taking away the feeling that you ''discovered'' anything at all. That combined with a fairly boring map layout rife with invisible walls, with little to look at that isn't the next point of interest, makes getting to the interesting locations very lackluster.
What you call the horseshoe, I've been calling the racetrack, and it's a great example of the design philosophy in this regard. Though I do believe while this hurts exploration, it helped Obsidian control the narrative's pacing. So it's a trade off.
Between 3 and 4, I think this largely depends on what you consider the point of exploration is. 4's crafting mechanics meant every building was worth investigating. And as you got further up the crafting tree, revisiting old locations took on new value as junk you used to overlook now contained needed components. That combined with the more dense, diverse, interesting and intricate building layouts, helped by improved verticality, meant for the first time in a Fallout game players were actually scavenging.
I actually prefer 3's exploration for much the same reasons you mentioned. But a friend of mine prefers 4 for the aforementioned reasons. And he clearly enjoyed exploring 4 as much as I did 3. To the extent that I'm not confident in saying either form of exploring is the ''better form''.
Visually speaking, overall I do agree that 3 felt the ''most Fallout''. Actually I prefer the original on this front, but we aren't talking about Interplay Fallout at the moment. Suffice it to say, the tone and visual story telling in 3 is its greatest strength, and hands down the best of the Bethesda era games.
Though 4's retro futuristic building designs are by far the most accurate to the setting of the original games. Which I appreciate. Especially since 3/NV are mostly just ''bombed out modern day'' aesthetics.
Which brings me to the discussion of Quest and Story designs.
We are going to have to agree to disagree on our opinions regarding the emotions brought about by the quests it would seem. While both 3 and NV occasionally have stories that fall flat, I would say 3 has far more of them that fall flat. For me, NV had far more that made me feel the emotion of the quest, leaving me with something memorable, funny, thought was awesome, and/or tickled my brain, with the added benefit of greater agency to make me "part of the story", and not just a passenger.
And tbh, I think you might be forcing your opinion a bit hard by making the claim that 3's narratives do this better. Just focusing on the side quest's, NV has far more quests that check the aforementioned boxes for me. You may not have liked Goodsprings, but an old west showdown where you have to rally the town? That absolutely tickled my brain in a fun way. Honestly similar to "The Replicated Man" from 3, where the take on classic movie plots was enjoyable enough that the incredibly flat story telling can be forgiven. The introduction to the Legion at Nipton, the lottery? Actually terrifying to think about. The Boulder City showdown, a high stakes hostage situation, actually awesome. Vault 11, Vault 22, all of the amazing companion quests, the Ghouls in Rockets, The Kings, the list goes on an on.
3 had some bangers as well, the Replicated Man, Tenpenny Tower, Agatha's violin, Arefu's Vampires, the Republic of Dave, the Canterbury Common Superheroes, Oasis, Stealing Independence. I actually think 3 doesn't get enough credit for how many fun side quests it had. But I wouldn't say they were definitively more memorable/funny/emotional/brain tickling than anything NV had to offer.
And NV had an extra trick up it's sleeve to elevate every quest. The inter-connectivity of the narratives. Where almost everything in 3 was taking place on a proverbial island, with basically no quests informing or impacting another, NV's quests all built off of and flow into each other in a way that meant the more you played it, the more impactful/memorable/funny/emotional/brain-tickling the others were thanks to their combined meaning.
The main stories however we flat disagree on. 3's Main story was... terrible for two main reasons. It was boring (which I get is just my opinion... but I'll elaborate in a moment), and its design directly took players away from the best elements of the game. New Vegas on the other hand has a far more interesting story, and used it to encourage players to engage with its strongest elements.
As for which story was more engaging, I get that this is opinionated, but I'll just start by saying I didn't care about the main story of 3 at all upon leaving the vault. It never gave me a reason to. I didn't care about finding Liam Nissan, and once I did it was by accident through exploration, I didn't care about project purity (Nor did anyone else, some folks worshipped radiation, and the rest seemed to only rarely be shown to be having any water related crisis), I didn't care about the Enclave, I didn't care about the BoS. They were all just so under written that I barely know why they were doing anything at all and I keep forgetting characters. And the story elements were so generic and uninspired that I was just bored. I only actually finished the story once Broken Steel came out, and even then just to see the new content and used the main quest to power level a new character. And the ultimate choice for all of that was "Do you want to commit a genocide by injecting FEV into the water purifier?". In the end, it was a poorly told story, with weak stakes filled with boring characters and nothing interesting to say. You may think people over embellish NV's shades of gray, but 3 didn't even have a compelling choice to ask the player. It was honestly the worst part of the game for me.
While NV also centers the plot around control of a resource generating installation, it uses this as a motivator to a far more intriguing exploration of the human condition. With better written factions and introducing a far more memorable cast of key characters. Compare House, Caesar, Benny, and Yes Man to Liam "your dad" Nissan, Lyons (both of them), Autumn and Eden. Now honestly tell me 3 had the better written characters with more engaging motivations and personalities?
Frankly, 3's main story fell super flat, and is usually left out of discussion on why the game was great for a reason, where NV's main story is still being discussed and debated to this day. So even if it's just opinions, the overwhelming difference in how many people feel strongly about it seems to imply we could take the average and determine which games main story made a "stronger impact".
And as an aside, I think you might have undersold the quality of the shades of gray in NV by simplifying it to the NCR v Legion dichotomy. The real shades of gray are found in how you decide the fate of all factions. It not as simple as who wins, but how everyone lives together after.
On to which game's main story is better "designed" from a game play perspective, this one is no doubt going to NV. To preface this, remember the best part of each game. The greatest strength of 3 was it's exploration, where for NV it was its narrative agency. 3's main story barely had anything to do with exploration, taking you to only a few locations. It would instead have you spending hours on engaging with the worst part of the game, i.e. the dialogue and the stilted attempts at "cinema". From the Vault intro, to Tranquility Lane, to the entire stretch of time from entering the Purifier with your dad until you make it to the Citadel, from the moment you get the GECK until you escape Raven Rock, and finally the attack on the purifier, all take you away from exploring the world and instead ask you to sit and watch the game at it's worst.
NV on the other hand constantly asked you to engage with it's strongest element, making narrative choices. Which may not be your cup of tea, but it's hard to argue it wasn't what people who do like the game love about it.
I meant to go on to game mechanics, but I seem to be hitting the character limit as well, so I'll leave those points for what they are.
Social welfare capitalism is good in theory. But social welfare is in direct opposition to capitalism, and there is no way to actually contain the corrupting power of capitalism. The social aspect will always get buried.