Safari has this setting, but the half dozen times I've tried it, it doesn't work. I suspect you're right that it's because sites just look at the resolution.
That's because trying to detect desktop/mobile is itself gross and hacky, as well as hard to work with as a dev. Just doing resolution-based stuff is easier, more reliable, and usually a better experience when devs aren't lazy enough to just leave things out in the smaller views.
Surely you don't mean to block our popups, right?
Surely you didn't mean to block our auto-playing video, right?
Surely you would rather use our lousy app rather than the desktop web site you explicitly requested, right?
etc.