I'm fine with a driver having an (unobtrusive, tasteful) tip jar in their car, but if a driver ever actively asked me for a tip, I'd give them a lower rating (commensurate with how hard they pushed for the tip) and report them to Uber for making me feel uncomfortable while captive in their car.

I use payment-in-app services in part because I don't like carrying much or any cash around, and when I do, it's usually just a few $20 bills, which aren't very useful for tipping in this scenario.

And yes, I do tip in-app when I use Lyft, in part because their social contract includes tipping, and I can do it without the on-the-spot pressure of needing to do so in the car. Uber explicitly states that tips are not expected or required, and does not provide an in-app way of tipping, so I wouldn't tolerate tip solicitation from a driver. (Hell, I wouldn't tolerate tip solicitation from a Lyft driver, either. Asking me for a tip when the app does it for you counts as "worse service" to me.)