In the UK it was solved by making all small transfers instant, while large transfers (direct debits, salaries) are still settled overnight. That way most of the transfers are instant while >90% of the amount transferred is still settled. Avoids issues for the banks' cash management while it's convenient for the user at the same time.
I think the US has the problem that it had to set up that way when clearing was done physically (due to the size of the country) and it's now very costly to change, for very little benefit to the banks.
While that's true, they're still mostly used for rather small amounts. The payment volume is around 5% of all electronic payments [1].
Not saying that Faster Payments are not a good thing, but they would probably cause problems for banks if most money would be moved by it. It works well because the major source of cash management is done due to card payments, direct debits and Bacs. So the normal cash buffer a bank holds throughout the day is sufficient to do fast transactions.
I think the US has the problem that it had to set up that way when clearing was done physically (due to the size of the country) and it's now very costly to change, for very little benefit to the banks.