a castlevania 3 remake seems like it could be a good idea instead of another version of sotn but shittier
Castlevania 1,3,4, and 5 really have a great mechanical feel that I think still could be meshed well with what the SotN and the games like it in the series have brought to the table. Castlevania 2 kind of hinted at that, but of course that game was broken beyond belief and can not sanely be played through without some kind of walkthrough (despite that I still liked it, and the romhack fixes for the NES rom show just how fucking awesome it could have been).
I think the SotN games do well in breaking the series of some of its rigidity, but their mechanics are so shallow at times it leads to frequent moments where the games feel watered-down. Like you said before, the second run in SotN where you can play as Richter are great and I think that is because it does a better job of meshing the game with the mechanics of the earlier games.
As for the show, I've not seen it yet as I've not bothered with Netflix in ages but it is really hard to screw up the Castlevania storyline since the games barely have one given their campy nature. That's not to say they can't or didn't make a terrible show, just that it's not like the games are forcing them into some kind of rigid framework for it since the games only have a very loose thematic framework anyways.