IMO there's nothing inherently wrong with two-day-old posts being on the front page. It's always bothered me that on reddit/lemmy it can often feel like there's no point of commenting on a post if it's over ~12 hours old because nobody will see it. It's one of the reasons I don't like news aggregators, the hyper-focus on constant new content is bad for community building and facilitating discussion.
Contrast this with BBS-style forums where threads can stay active for days, weeks, or even months if people are still engaged in a particular subject. You can get this same behavior on lemmy with the "new comments" sort mode, which I find preferable to these nebulous sorting algorithms. You get a mix of new posts as well as old ones that people are still discussing.
But really I think the best sort mode to use depends on the specific community. It makes sense for a news comm to prioritize new posts, but a meme comm should maybe prioritize upvotes more. More niche and discussion-based comms should prioritize engagement. IMO lemmy should allow for community-specific default sort modes.
(btw I don't disagree with your point that 'active' and 'hot' could be improved, I just don't think any particular sort mode is going to be best for all situations)