Personally I would have a hard time suspending disbelief if a story set in 2200 didn't have super-human AI and all diseases cured. Similarly there should be no pollution or over-population, at least in first world countries.
For humanity to avoid achieving those things, there would have to be some significant barriers to progress that we don't know about yet, or a fairly disastrous collapse, which would limit the possible stories that could be told.
I suppose that setting a story thousands of years into the future allows there to have been multiple collapses and renaissances, but I'm not convinced that such a path is as likely as a permanent collapse or reaching some sort of uninterruptible paradise state.
For humanity to avoid achieving those things, there would have to be some significant barriers to progress that we don't know about yet, or a fairly disastrous collapse, which would limit the possible stories that could be told.
I suppose that setting a story thousands of years into the future allows there to have been multiple collapses and renaissances, but I'm not convinced that such a path is as likely as a permanent collapse or reaching some sort of uninterruptible paradise state.