You seem to have unspoken assumption that propping up dictators actually make us safer or more prosperous.
This assumption is very popular among the powers that be, because it gives them a moral standing for being ruthless monsters: Their monstrosity protects their people. It even creates a self image that they are sacrifice themselves to make the world safer for their people. The same thing happened with the American slave trade: At first it was to help the poor uncivilized Africans find Christ, but when the slaves started converting to Christianity, and the slave owners did not want to give up their "property", they created the myth that Africans were stupid and childlike, so the slaves needed a firm hand (a.k.a. slavery was a good, Christian thing to do).
But that was a detour. Back to the issue at hand, we could start with an example: Iran. In 1953 the US and UK conspired with the Shah of Iran to bring down a democratically elected government (oil), and institute the most vicious dictatorship in the Middle East at the time. The Shah continued in power until he was overthrown by the 1979 revolution. When the dust settled, and the Islamists came out victorious, US ally Iraq invaded the country. Naturally, the people of Iran knew of the role that the US had played, and hated the country for its crimes against Iranians. Even now relations are strained to say the least. Iran is allying itself with Iraq, and the US and the UK is on the sidelines, slowly but surely loosing ground in the oil rich Middle East. *That* is the price of instigating the 1953 coup, and I doubt the US and UK are done paying for that nasty business. Fortunately for the physical safety of westerners, the rulers of Iran are reasonably sane, and neither train nor fund terrorism against Western targets.
Which problem do you want to solve?