Uber charges you for "wait time" after you request a car...which is insane. Not that Lyft is much better, but I've never seen that kind of nonsense with them.

How is it nonsense? Someone is using their time and fuel to get to your location. It's only natural you pay for it.

It feels like they're double dipping. Unpopular as it might be, I'd guess people would be more than willing to pay extra so that they could shitcan this "feature".

So you want to pay extra to not pay extra?

Yes. Paying extra for the service itself, not an arbitrary charge that could vary greatly at any time seems worth it.

I don't think it's arbitrary. You're paying for the (vehicle, driver) time and distance and the closer your are to vehicle the shorter the trip. If the vehicle is far enough away to make it vary greatly just cancel. The seemingly arbitrary charges and price volatility are not supposed to start until after you're in the vehicle. This may just be a bug.

In my case I stood there in the rain for 15 minutes waiting for a car that never came and eventually canceled, so I walked around till I got to a taxi stand. A little less than magical.