Besides being historically grown like that, I see two major differences to the rest of the world:

Credit cards have no PIN in the US (and debit cards can usually be used without one as well), which makes this approach possible in the first place, and the tipping culture that can make it desirable to get a quiet moment with the check to figure out amounts.

Practically, it also means that even larger restaurants usually only need very few POS terminals at a central location, rather than one per waiter, requiring wireless infrastructure in larger restaurants etc.

This is changing very fast, though – I‘m seeing both combined order and payment handheld devices (that support tap-to-pay, i.e. also Apple Pay) as well as the QR payment solution in more and more places.