And yet I see nobody on these forums use that or Cyrod other than people friendly with the lore. 
And, wait, did they? In Oblivion? I don't remember that.

And, wait, did they? In Oblivion? I don't remember that.
Eh, it was in Morrowind, other races would refer to you as "Cyrodil".
In Oblivion, some NPC's would say "Did you want to talk, or are you just practicing your Cyrodillic?", or something of that nature. This would infer the traditional term for natives of Cyrodil is...Cyrod, or simply Cyrodil...and that the term Imperial is simply the term used by those outside Cyrodil.