"Biting the bullet" is a good idea, if you have the bullet. However, if the bullet is being supplied by a friend (like the USA), then one has to listen to that friend and especially if that friend is just about the only important friend one has in the entire world.
Because, if that friend doesn't like what you do and doesn't give you any more bullets you won't only lose the Temple Mount, one would lose one's entire country and every precious soul in it.
Doesn't pay to anger important friends.
Especially when you are one of the smallest countries in the world (Israel is the size of New Jersey) and is surrounded by enemies who command over a billion people who control a vast amount of the world's wealth.
The results of both options are likely to be the same; it's simply a matter of which takes longer.
The choice then becomes one of, do I want to disappear actively trying to destroy my enemy? Or slowly and painfully fading into history to placate a doubtful "friend"?