Taxis don't only exist due to cost. It's more convenient to take a cab across London because even if you have unlimited money, finding parking is a pain in the arse, you have to think about it, etc.

Or you might just be tipsy after a night out.

I've never taken a cab to save money; I'm not sure I've ever been in a situation where it would be cheaper than just taking public transport or driving.

It's just a different option with different pros and cons.