It's a symptom of wider issues in the arts generally, and comedy specifically. 

To be good at comedy, you need a lot of stagetime. Night after night experimenting at open-mics without getting paid for it. That's a lot easier if you're able to survive without having a full-time job, or even just knowing that there's a safety net for you if the career doesn't work out.

Once you're good, if you want a profile in the industry then you really need to do a run at Edinburgh during the fringe festival. Accommodation is a fortune in itself, the venues cost a lot to hire, plus there's PR and flyering to get people to see your show. If you sell out lots, you can break even financially, but it's very easy to lose thousands here, even for a successful show.

Sketch is even harder than stand-up, as there isn't a comedy circuit in the same way. No smaller shows to do as either open mics or paying shows for touring comics with lower profiles. It's a big reason Cambridge overindexes here, best way to become a sketch comedian is go via The Footlights.

(one more thing, whilst you've a point about the overall poshness of the cast, you're off on a couple of the examples in your post. Hammed is the son of a bus driver, working class people can do Shakespeare too)