I don't think the lack of such a system in the US is for the reason you think - all you do is tell your bank to send money to the account attached to whatever phone number you enter so it should be technically possible.

As a former resident of the UK my feeling is that the lack of such system there is because most bank apps have traditionally been shit. Its probably better today but back in 2015 (when Blik launched) I would not have expected to do anything useful with my bank's app.

For something like blik to work well you need every participating bank to already have a decent mobile banking app and for them to be willing to put in some time/money into integrating the new functionality with that app. Blik started because a bunch of the biggest Polish banks got together and between them founded a company to launch the service. Its really hard for me to imagine the 6 biggest banks in the UK getting together and doing that.

Poland's banking industry also skipped a bunch of "cruft" that we have in the UK because it started after we'd already progressed past those things being relevant. My Polish bank card doesn't have a "sort code" to identify my home branch (because who the hell cares about that in 2024), Poland briefly had cheques but stopped having them in 2006 because everyone was already using cards. In tech-industry terms the UK banking system has a bunch of "technical debt" it has to work around.