I must admit, when I got my 144hz monitor I was excited, coming from a 60hz monitor. But even if a game runs at 144 fps I don't see much of a difference, many people do, but I don't. It's a bit smoother, but not much.
But if a game runs at 30 fps it's horrible. The Crew, for example, can be switched to 30 or 60 fps, that's night and day!
It's super dependent on the game. Baldur's Gate 3? 30 fps is more than enough. League of Legends? Yeah, I'll take those 144hz, tho to be honest I don't notice a big difference compared to 60 fps.
Yeah, 144hz makes a significant difference for competitive FPS games (especially fast paced ones like Overwatch), but I hardly notice a difference when playing single player or PvE oriented games.
Hell, on some games (e.g. Borderlands 3 and CP2077) I actually prefer to play on my 60hz monitor since a smooth 60hz is much more enjoyable IMO than an inconsistent 100-144hz experience. My computer is admittedly pretty old though.
You can cap the fps in software, no need to switch monitors.
Also personally I always notice the difference, even when scrolling webpages