I've lived in London since 1995, and minicab drivers have never lied to me, and I've taken a shit-load of them in that time.
For a start, in London you don't agree the price with the driver, you agree it on the phone with the head office or you agree it in the local office if you're a walk-in. So what's to discuss with the driver? And how does a lie like that even work? "Oooh, tricked you, I said it was a tenner and it's actually fifteen quid!" "Er, well I agreed to a tenner, not 15 quid, so I'm paying a tenner".
As for your other complaints: the vast majority of cab firms now allow you to pay online with a card, so you don't have to argue about cabbies not having enough change.
I notice you only picked out one aspect of what I wrote about in the passage you quoted, by the way. I also highlighted that minicabs are required to be pre-bookable. Uber chooses to ignore this requirement, which was by itself the reason I gave up on using them. When I need to get my son to a football match at 9.30 on a Sunday morning from our house in the London suburbs, I want to be sure the cab will be there at 9.15. Uber are completely unreliable for this, because funnily enough, there's not much liquidity of supply at 9am on a Sunday in zone 3.
I stand by what I said: Uber don't offer firm pricing, they don't offer regulated metered pricing, they don't offer pre-bookability, they don't meet the behavioural regulations that benefit passengers (e.g. cab-rank obligation to carry regardless of destination, public liability insurance), nor the vehicle requirements (e.g. turning circle), nor the driver requirements (e.g. enhanced DBS check, the Knowledge). They are a crap mix of the least beneficial aspects of minicabs and taxis, operating in the interests of their investors much more than their passengers. But they are -- for now, and when surge pricing isn't switched on -- cheap, and they are reasonably plentiful. So they're reasonably popular.