I wouldn't call any of his games "deep," with the exception of maybe Silver Case. There's honestly nothing obtuse about them, they're extremely straight forward and juvenile and that's basically the appeal. The reason I can't recommend these games is because most people these days are complete faggots. They want to play a "deep" game with secret messages and THEMES, so they can wank off over it later on reddit and impress everyone with their big analysis brain. When these people encounter something out of Grasshopper, they note the weirdness and think "Oh man, here come the themes, unf, META, unf unf, I'm gonna GAME THEEEEEORY!!" only to end up frustrated that there is actually very little going on beneath the surface. That luchador that you keep running into isn't a metaphor for the main character's secret homo thoughts, it's literally just a luchador and also he's cool. The "gigolo minigame" isn't an elaborate criticism of the male gaze, its a minigame where you give girls gifts and then peek at their tits and nothing more.
I agree the controls in the NMH series are jank due to being designed originally with waggle bullshit, but otherwise I've found every Suda 51 game responsive and very entertaining.