Yes, I'm sure Sheff Utd and the player would have gone along with that.
Naughton's about to make the biggest decision of his career. If he would be wiling to make that decision without even being allowed to find out which other clubs were interested, then he's an idiot. Luckily, he agent won't be that dumb.
These transfer sagas go on at every single club in the league/the world. You might as well say "why didn't Spurs wrap up the transfer for Naughton a month ago, before Everton were interested, so they didn't have to get involved in an auction?"
And, of course, you are ignoring all the transfers where we just signed the player with little trouble. Baines, Jagielka, Lescott, Cahill, Beattie, Johnson - all signed with no protracted negotiations. With Arteta, there were delayed negotiations, during which we negotiated the price down.