The irony of letting the public vote would be that it would actually turn into a popularity contest.
LAWL
Yep, and it would make it like every other stupid reality show out there. We might not always agree with what the jury decides, but I think it's a MUCH better method than having America vote, which turns into a popularity contest rather than who actually deserves to win. I've been far more frustrated by whom America chooses to win reality shows than whom the Survivor jury chooses.
If you look back at Survivor: All Stars, Rupert won America's vote (and $1 million). Did he even come close to playing the best game? Absolutely not! If anyone should've won, it should've been Boston Rob for the great game he played, but America voted for their favorite.
Also, if the tribe knew there would be no jury and America would be voting, then that would change the entire season. It's not just the final tribal council that would change. People would be trying to make their confessionals more appealing to America, not caring what their tribe thought of them, etc.
Whether I agree with their decisions or not, having the final 9 sit on a jury to vote for which finalist wins is a quintessential part of Survivor. As Jeff said, without the jury it wouldn't be Survivor, it would be a different show altogether.