The problem is that the US is rather larger than the UK, so a distributed system was (and maybe still is) a natural fit. For the same reason, all the citizens of the US can't just come to one place and vote for a President, like ancient Athenians could.
Basically, you can tell from the routing number on a check where the bank is. Back in the day, if the bank wasn’t from NYC or the same region they wouldn’t honor the check. Checks were mailed between clearing systems and would take weeks to clear. My dad maintained a bank account at the Bank of New York specifically for business travel in the 80s.
That’s mostly gone now as ACH is automated and quick.