Yes, of course. If your TV doesn't support 4K at 120 Hz but it does support 1440p/1080p at 120 Hz you can play at 1080p@120fps. No problem. I don't think it's worth the hit, but the option is there.
Sorry, that's not true. 60 fps was and still is the standard for 2D games, but ever since the 3D arrived 60 fps has never been the standard. In fact most games ran terribly and well bellow 30 fps. On PSX there are 110 games out of 4.105 that targeted 60 fps (and even fewer hit that target). On N64 it was even worse and only 9 titles that I know of (out of almost 400) targeted 60 fps, but most games ran very poorly, things like 10 or 15 fps were quite common. . On the next gen things were better but still far from 60 fps as standar. A few great looking games were 60 fps (Devil May Cry, Metroid, MGS2) but most targeted 30 fps: Metal Gear Solid 3, GTA series, Super Mario Sunshine, Zelda (both) , Halo 1 and 2, Final Fantasy X, XI and XII, ICO, Shadow of the Colossus, Resident Evil (all of them), Silent Hill (all of them again), Okami, Dragon Quest, Persona saga, Princesa of Persia, both Pikmin, ... you name it. Contrary to popular belief things looked up in the next couple of generations, we just started caring about 60 fps. This is the first gen where most games are 60 fps. Almost every game, in fact. Something we hadn't ever seen in any previous generation.