There aren't a lot of situations where, if I want to play a game, I'd choose to play it on a small screen with a worse resolution than my PC monitor, and I often find that playing games for long stretches on handhelds can get really uncomfortable; my hands just naturally don't like using a handheld system for too long, or maybe that's a problem specific to my current handheld, the 3DS XL. But if I'm in bed, or watching something on TV/my computer, or on a bus, or whatever, then yeah, I'll fire up my 3DS, but I'm not playing games like 40+ hour long RPGs, with a couple of exceptions. Also, games with a lot of interface i.e. games with a lot of menus and information they have to convey, like Civilization or Crusader Kings II, just don't work on handheld systems. In fact, a lot of genres just don't work at all on handhelds for me.
PC is my preferred way of playing games and I don't see that changing any time soon, but there is certainly a place for handheld games, and certain genres of games thrive on handhelds. In theory, there's no inherent reason why games on other platforms are better than those on handhelds, except for obvious graphical limitations, but in practice, very few of my favourite games are handheld games, and I owned every iteration of the Game Boy when I was a kid, from the original up to the Advance SP.
Side-note: I picked the PC master race option, but I don't actually only like PC games. I like console games and handheld games as well. PC is just my preferred way to play games.