Well besides it being even more reminiscent of the British Empire (sun never sets eh?) then we already have, you've just added 5,000,000+ people to the tax base, to the Social Security system, etc. Then you're going to have to convince them to follow our form of government and our laws. LOL, that ought to be fun. Not to mention the fact territorial disputes, etc. Our Armed Forces would literally be stationed there year round in defense, you'd have at least two whole fleets in the Med region just for that alone. How do you think the Russians, Chinese, et. al. are going to feel about that?
I'm just scratching the surface here. It simply would never work no matter how you feel about it. Unless you've forgotten Republicans are supposed to stand for limited government and your one move would at least double (if not triple) the size of government and the bureaucracy we currently have
Perhaps we should just surrender to communism/socialism now since our laws and form of government are so weak and unappealing?