But none - absolutely none of the arguments you've put forward preclude the idea, or even discourage the notion, of a Gallifreyan working class. Not a single one. Yet you're behaving as if your reasoning is impeccable and we're all morons for not subscribing to it.
I just googled Gallifreyan working class and came up with a link to this novel.
The Eight Doctors; by Terrance Dicks
http://www.drwhoguide.com/whobbc01.htm
In the continuity notes at the bottom of the page it says:
The Shobogans were first named in The Deadly Assassin, and this novel confirms that they are, in effect, Gallifrey’s working class.
I guess non-cannon but maybe interesting.
Apologies if someone has already gone over this I couldn't be bothered trawling the whole thread.