I live in the UK. Can't say I agree with you. Especially because I have a mobility impairment. The Uber drivers are always more willing to help, (I'd imagine thanks to the rating system), stop exactly where needed etc.
In London - I'd say cabs are better. In Liverpool and Manchester, I'd say on par with Uber.
Didn't have experience with Assist and Access Uber cars, so you have a better view on that.