HoMM3 HD bug reports.

Yes. But for online play, it would be better to do the following:

1) Deceased, dismissed, and otherwise unavailable heroes cannot be bought back on the same day.

2) When the day changes, all heroes (including those in the tavern) have their movement points set according to their army. Artifact bonuses are not taken into account, and temporary bonuses from visiting buildings (e.g., stables) are reset. Mana is calculated based on the hero's native Knowledge skill, without considering artifacts.

The situation where players buy and search for deceased, dismissed, and other heroes with 2000 mana points and other bonuses is very common. And it has even been captured on video (e.g., the "Tvarina's Treat" video). No one complains because they understand that it could backfire on them, but otherwise, it can sometimes be a lifesaver. If the bug is to be fixed, it should be done completely, with stats, knowledge, bonuses, and artifacts being reset (as it should be and as is fair). Or it should not be touched at all (but then you have to hope for a miracle). And what is the great point if they cannot be bought back on the same day, but only on the next? In offline mode, there is a 100% chance of buying them, but this is not the case in online mode. And finding a mega-hero in the tavern really does seem like a miracle (while costing a hundred or two thousand gold and a lot of time), and that's what makes it enjoyable. And what an intrigue!
A much more unpleasant situation is when you buy a hero with zero movement points – this is where it really needs to be fixed.