What do these 'sending money to people' systems do more than that?
To buy something online using blik your bank's app generates a 6 digit one time code which is valid for something like 2 minutes. You enter that on the website of whoever you're trying to pay rather than give them your card number and cvv. This is nice because in addition to being a lot shorter to enter than a card number a nefarious person can't reuse the code to perform more transactions at a later date (since they don't have your card number).
The phone number is an id into the bilk system.
With bank transfers both parties do not need to be register with an app they just use the id that they have already for other reasons the bank sort code and id. So needs less extra infrastructure but the user interface is more unfriendly (people don't remember their bank account number).
Now if banks linked your phone number to the account number and sort code.....
There is no separate app for blik (at least as far as I'm aware) the functionality is integrated into my bank's app.
I do know why it is not in US as giving bank account details to others allows other to withdraw from your account.
This is not true in the UK so why no similar system here?
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.
But the bank never had any branches and was phone only from the mid 1980s and then had a web front end I think in the 90s.
Thus they knew what people needed before they wrote the app.
Edit: yes I am familiar with the various 'sending money to people' systems in Europe, but they don't rely on a debit card for the most part, rather, your bank account