Get their title, conquoer their land, become more dominent in their country. Use their disadvantge to our own. If their offering these honarary titles, then give them to us! We are a capitalistic country, we need more of everything. So thank you for support to allow United States citizens to hold British titles.
I can understand this being a problem in the decades or even century following the American Revolution, but at this point, the monarch of the UK is merely a figurehead that holds no real political power. Being knighted is no different than the President of the US giving a Medal of Freedom to a foreigner. It is recognition for achievements and has nothing to do with class or aristocracy. This is all not to mention that the UK and US have a special relationship following WWII.
Yes, I think it's all right for the United States government to let its citizens keep titles bestowed by Great Britain or other nations. A title is more symbolic than anything. It doesn't necessarily grant special powers. If it does, then so long as these special powers don't conflict with being a United States citizen, I don't see a problem.
Though individuals may be citizens of the United States, the government should not have complete control over their lives. This means that people should be able to hold whatever titles they want to hold, and the government should not have the power to prohibit them from holding British titles or titles of any other nationality.
Now obviously nobody in America is going to be the Queen or anything, but I don't have a problem with people being able to have titles. If any American should be a knight, Bill Gates should be a knight! Mostly though it's just an honorary thing, and doesn't really have much affect going forward.
I do not believe that the United States should allow its citizens to hold British titles. I believe adopting such a practice would only further highlight the social issues this country needs to address. These titles would make classism all the more easy and widen the already distant gap between the haves and the have-nots.