>The use case for a taxi is surely dominated by when you need a car but can't or don't want to drive? I've definitely taken more taxis near my home than away from it, purely because I'm here more often.

I'm sure it depends. I've never taken an Uber near my house. (I do get driven to and from the airport but I use a private car service for that.) I don't actually use Uber/Lyft (or taxis) all that much when I travel either although I've started to do so a bit more often when I found I mostly rented a car to get to/from the airport to some destination and then just have it sit.