Some genres suck in 2d, others in 3d.
Arcade shooters need 2d because it's much harder to aim in 3d, resulting in autoaim. It's also much harder to create bullet hells because the player can move up and down but when a cluster of shots is approaching you it's not possible to see their exact positions in 3d space (the problem has been in Stardust already and that was all sprites!).
Fast moving games work better in 3d because you can see into the distance while you are constrained to a rectangle with 2d and Sonic can move across the screen in half a second. It should technically not be possible for 2d Sonics to be better than 3d ones if speed really is an important factor (as you can't see crap when moving fast in a 2d Sonic) but Sega sucks so bad they couldn't figure out that they should take inspiration from racing games, not Mario 64 (I hear they fixed it with Sonic Wii, though).
IMO Zelda works better in 2d because of the targetting, in 2d you can just press fire and know your shot lines up, in 3d you have to stop and aim first, you get autoaim and all that instead of just drawing your bow and firing because you know it lines up. Also the 3d Zeldas have too much "use item A, then B, then C" fighting while e.g. LttP doesn't even give you a new item in every dungeon, sometimes you just have to beat bosses up with your sword instead of spamming whatever new item you got.
RPGs can use anything because it has no effect on the gameplay anyway, they could be text based and still play the same.
Anyone remember Samurai Showdown for the Neo Geo and arcade? It's an old-school game that featured large beautifully hand-drawn warriors fighting in well detailed environments that zoom in and out when fighters moved toward and away from each other.
Nope. I do remember Samurai Shodown 5 for the PS2, though. I hear Nakoruru has quite a fanbase.