You are confusing "being despised" with "lack of stability".
tell you what - you tell me. which is less stable: Egypt under Mubarak, or Egypt under the Brotherhood? Easier version: which was less stable: The middle east during the 1950s 60s and 70s when nation-on-nation war was a constant occurrence, or the middle east in the 90s once we turned the arab states into client states, and the single big conflict was us v Iraq and then isralies and palestinians bickering? Was Egypt more likely to go to war with Israel and Saudi Arabia under
Nasser? Or Mubarak after we decided to start supporting him?
For that matter, which is less stable: Jordan, under our ally the king, or Gaza, where the Palestinians rule themselves?
Which is less stable: Saudi Arabia, whom we have poured massive resources into? Or Yemen, where we haven't?
The single example of Iraq actually
makes my argument - the only reason we supplied Saddam is because we wanted to stop the
destabilizing force of Shia Islamist Revolution from spreading to other Shia-dominant areas (such as Bahrain). We backed Saddam at the time
because that was the stabilizing option in the ME.
You'll get no argument from me that our policy of supporting abusive governments is a large part of why we are hated. Agreed. But arguing that dictators aren't generally capable of controlling their space doesn't match the historical record. It's a relatively short term (it only lasts for a generation or three) solution; but it
is a solution.