I don't agree with the part about the Police but I definitely agree that Culture Club's catalog is very sturdy for pop music.
Might just be my bias against that particular style, but I'm afraid I'll disagree here.
I personally think the only song from the Culture Club discography that has stood up to the test of time is "Do You Really Want To Hurt Me". The rest I think lack any lasting appeal whatsoever, personally.
While, for me at least, the Police discography doesn't sound dated at all (although I'll admit Roxanne can get annoying pretty quickly).
I'm afraid, if I was looking to hire a songwriter for whatever reason, I'd pick Sting over the entire Culture Club any day of the week personally. (money permitting, of course)