I have never had a problem with the cabs where I live (and Uber is banned)
Anyway to add my anecdote as a counter to yours. I was back home in Scotland at Christmas last year. Private Cabs were all busy, so we tried an Uber wanted to charge nearly three times what the monopolistic black cabs (the ones you hail from the street) charge. My one and only experience with Uber and it didn't seem good.