Akwizgran? Don't you mean Aix-la-Chapelle?
Seriously though, I think there's more at stake here than just political correctness.
It all depends on context. In an English conversation, the use of Roma or Warszawa or Moskva would be pretentious.
However, in a public context, one has to bear in mind political sensitivities. The different forms of names for towns carry political and historic connotations whether one likes it or not, particularly in eastern Europe and the ex-colonial world.
In atlases, gazetteers, timetables, road maps etc. is makes sense to use one standard form, and that being the form the user is most likely to encounter, i.e. the native form.
Nevertheless, there are instances of the lunatic extreme of political correctness in all this - Baile atha Cliath being one in my opinion. The worst case I know if is in Wales, where all road signs are in Welsh (first) then English. This makes for very large signs, and for a potential driving hazard when you're trying to find your way. Of course, this had to be done because, while all Welsh people speak English, only a minority speak Welsh.
Just for your info, neither the name nor the pronunciation of  Beijing has changed. All that has changed is the transliteration system used. The old system (Wade-something-or-other) rendered it as Peking, which led to it being pronounced like "peeking".
 
Cheers
Dennis Poulter