> how hard could it be to enforce rules?

See the recent events and pushback on immigration enforcement, to answer this, white whole cities (with their c judicial system and and police included) refusing to participate, and governors condemning enforcement.

> They know who you are and where you work

Most visas don't permit their holder to work.

> Wait, what’s getting enforced here, anyway?

The visa holder is forced to expend nominal financial resources and time in their home country (where they agreed they would return to.) Most people can't afford to maintain a facade of residency or two actual residences (and those who can aren't the intended targets of this type of restriction.)

No, not necessarily. Sometimes visas are rejected. Unless you're talking about giving everyone who gets a visa a green card?