I'd say it's a question of what you want to achieve as an experience, versus what you can reach. Below thirty frames per second, there's not a single title out there that could qualify as being playable. 30 FPS is the absolute minimum to reliably enjoy anything related to games.
If you can crank your FPS count to higher and have it reach sixty, then all you're doing is getting yourself some extra comfort. Animations are going to look more fluid, movement is going to feel entirely natural. Lifelong gamers could tell you that 30 FPS still does feel a little artificial. There's an undefinable... "something" the eyes start picking up that makes the experience uncomfortable. Minuscule hiccups between frames, maybe. I've had that impression, but I can't quantify it.
Then there's the fact that nowadays, 30 FPS is borderline. The game works and doesn't chug, sure, but if it ever drops below that, all bets are off. I personally consider the sixty-plus mark to be something that's mainly there to give me some breathing room. That way I won't jump between moments where everything's smooth as silk, and other moments where my rig goes "HUUUUUUURRR, RENDERING EACH FRAME AT THE SWEAT OF MY FREAKING BROW, AAAARRRGH!"