I've always suspected they don't, but the cab driver says it's not working so you pay cash that they don't to declare as income in order to minimize their tax liability. I have no real basis for this suspicion though, besides knowing that taxi drivers were notorious for tax dodging before card readers were common (like most cash-based businesses really).
Same in restaurants. They hate it when you pay with your card. They love untaxed income and I don't blame them.
FYI my understanding is that, in London at least, cabs aren't allowed to operated with a broken card reader; if that happens to you, tell them that you have no cash and either it will suddenly magically work or you'll get a free ride (this has happened to me).
When I ask to pay by card in the UK or Norway, it's 50/50 whether the driver claims the card machine is broken. If you say you don't have cash, they're like "oh, well, let's try just in case", and lo and behold, it works every time.