I did try asking for a PWP as my birthday wish. I did end up getting it (the police station), but over a month after I asked for it. I think the fact I got it was a coincidence and nothing to do with the birthday wish.
I actually have no problem paying for any of the PWPs, rather the diving trick never helps me in getting the request from them. No one ever "pings!" at me, ever. So I'm playing through the game & waiting for them to normally ask me. Last night was my first PWP request in a looooong time.
So yes, that would be so useful as a birthday present. <3
My villagers have gotten so much better asking for PwP. I did the diving trick a few times but it took awhile and a lot of going in and out for me to get something from it. Now it happens when I first play my day, someone would randomly ping me before I even move an inch. I'd get something suggested everyday for a few days and then get nothing for a month or so.