I don't know if you've noticed this, but threads or comments about Lemmy or the Fediverse get downvoted a lot on Reddit and trolls who claim that it's "dogshit" and "not going anywhere" get systematically upvoted.
Some of those trolls get then exposed when you ask them what Lemmy instance they tried and one of them with whom I had a surreal exchange answered with something like "yeah ofc I used Lemmy, this is the instance: join-lemmy.org" 🤦♂️
It's frustrating that these trolls keep contributing to the big lie that "Lemmy is not ready yet" and that there's "no viable alternative to Reddit".
This and the overwhelming number of comments being "against the mod protests" just prompts me to question whether there isn't some brigading being organized straight from the Reddit HQ.
If you're coming from anywhere other than your home instance, that's a slightly different problem that is unfortunately impossible to completely solve without a browser extension. Sites cannot access cookies from a different website for obvious security reasons. So the most another web site would be able to do is offer a drop down with a redirect to the most popular instances. It would work similar to third party social media sign-ins (e.g. sign in via google account).
The problem with the fediverse is that they couldn't possibly offer a full sign-in list, but maybe at worst you would have to type it in manually or rely on an extension.