Well, I can't disagree with the reasons, but as someone who lives outside the M25 this means I lose a really handy way to get home when I've had a drink. Ah well, I'm supposed to have given up anyway :-)
You're looking at roughly twice the cost, usually more if it's late on a Friday/Saturday night. I used to regularly travel from Zone 1 to just inside the M25 to the West of London ─ an Uber costs ~£40, whereas I've paid between £80 and £120 for other private hires for similar journeys.
4 miles in a black cab summoned via Hailo can cost you £25 on a Saturday afternoon as a price comparison. It takes 15 minutes for them to turn up and the journey takes up to 30 mins or so depending on traffic.
I can actually walk that in under an hour if I need to.
If/while you still can, you might as well just walk (or take a bus, they're great)! London is a beautiful city, with myriad hidden wonders that you just don't find unless you're on foot.
I've found myself in countless situations where the walk is maybe 10-15 mins longer than any available public transport (Uber included), so I've saved myself the money and taken a hit on a little bit of time.