All major banks participate in it, and it's both P2P (send to target phone number, which will behind the scenes resolve to a bank account) and web payments (use a one-time code from your bank app and then confirm in the app, without sharing any permanent data like card numbers).
Also, it's instantaneous and free.
And in fact almost nobody in Poland uses Revolut nor PayPal for P2P, everybody uses BLIK. People do use Revolut for their great exchange rates though.
No, participants have nostro/vostro accounts with each other, and payments are immediately settled using those. Participants shuffle money between those, including via accounts at the Bank of England if necessary, to maintain sufficient liquidity; they do that throughout the day, with a big cleanup at the end of the day, but it's not part of the transaction.
Which means that banks need to keep track of their balances with other participants, and not send customers' payments if that would take them overdrawn. Obviously this would be highly undesirable, so they work hard to keep those accounts topped up.
For non-P2P stuff like PayPal is very good because bank transfers are non-reversible. You can do G&S on PayPal and reverse that if you need to.
For P2P, stuff like Revolut, PayPal, whatever is still easier because you don't need to remember your bank account number. There is also no interoperability between banking apps either (the only interaction is through FASTER and your number). So you end up needing someone in the middle, like PayPal, which (in the end) is just doing bank transfers...not ideal but it is, at least, cheap.
Reason would suggest the latter will eventually change, but that day is not today.
Also, cross-currency transfers are significantly easier with apps. I agree that it is all a bit unnecessary but...banks are banks. In the UK, there has been a lot of competition and services are still (imo) dire.