2-3 years ago they changed something and I know tens of people (and I don't know that many people) say that now filling in bank details in the SA itself has become a no-op, and that they (and I) now had to explicitly request a withdrawal of the balance. Often 2-3 times.

And it's not been a matter of waiting. The money just sits there for the better part of a year before people have noticed.

Yes I have also received payments for refunds of PAYE automatically within a month or two of no action on my part.

Yeah, this has been my experience too. I don't know how much easier it could be.