I have to remember to fill up my gas tank to use my own car or charge my phone to use Uber. Both of these tasks require similar amount of work as reloading a public transport card online.
Not only is charging your average smartphone far easier (one wire or just dropping it onto a pad) but most people find their phone is necessary for other uses as well, so using it for Uber requires no extra work.
> I have to remember to fill up my gas tank to use my own car
By that time you're already in your car, there's friction but there's probably more friction to finding an alternative mode of transportation than to stopping at a gas station.
> or charge my phone to use Uber.
You're likely using your phone for many other things and charging it every night if not more often, you don't have to charge it exclusively for the purpose of using Uber.