As annoying, to me, is that Godaddy lets you go through the entire transfer process without TELLING you it's going to be rejected.
So you have to the transfer get it rejected, THEN turn off privacy, then do it all again.
On the other hand, that just makes it that much sweeter once the domain finally lands at Route53 (etc) and you no longer have to play Godaddy Renewal Roulette and wonder if your next renewal will be 50% higher than normal.
(Oh, and BTW, I was happy to see that if your domain registration is a company, Route53 does quasi-private registraiton at no extra cost.)