Well Pole almost made it in 1549... And he had closer ties with the English Kings... He even had his own claim to the English throne...
So why not Wolsey?
I'll take your word for how close he came, but the situation's a bit different. Wolsey was Henry's man through and through. Pole wasn't close to Henry at all, and being a Plantagenet claimant would have been an extra negative from Henry's viewpoint.
In fairness, sometimes someone with very close connections to one of the
continental monarchs was elected pope, Adrian VI for example. Since the French weren't able to block that one, maybe it would be possible for Wolsey after all.