I think this the relevent blog post for you:
It’s not so much that the idea of them planning to get a monopoly then hike prices makes sense, it’s just that it’s the only idea anyone came up with that even halfway makes their business model vaguely plausible.
Hiking prices is in any event a bit of a shorthand.
It would also require getting rid of all those pesky regulations you mentioned (notably, in London, Uber wasn’t prepared even to be governed by the sort of regulation you referred to as “being essentially open to anyone with a car, a driving licence and no criminal record”).
That of course indicates one reason multi-billionaires might be prepared to funnel billions into Uber, if it is one pressure point to attack what they see as unwarranted and improper government interference in their beautiful ‘free market’.
Once you have got rid of the regulations that stop you from achieving your monopoly, you of course immediately set about ensuring a regulatory background that keeps you in place.
For examples, see Uber’s car standards changes over time.
You can easily imagine a scenario in which if Uber somehow managed to acquire industry dominance, all your prospective mini-cab drivers are unable to obtain a vehicle that meets the new ‘minimum car standards’ requirements Uber managed to get put in place at a price that makes it possible for a newcomer to meaningfully challenge Uber.
Much in the same way black cab drivers complain about the fact that they can only buy a particular kind of car and how expensive they are.
Edit to add:
Would it work? If you’re dubious - congratulations, you apparently have more sense than the VC’s who bankroll Uber.