1. Many people do tip Uber drivers, but it's a pain to carry small bills and thus people who might well tip do.
2. Lyft does this and as it competes in the same pool for drivers, which one would you select if you are a driver?
3. It's the right thing to do in the US. Without going off onto one of those juvenile arguments about "they don't tip in my country, so I shouldn't tip here" it's just a part of life and cost.
Lyft permits the tip to be added for up to 24 hours after the ride and Uber claims that it will be permitted for up to 30 days. I don't think that drivers have the option of rating a passenger after the ride is closed out.
So, don't tip because you are worried, tip because it's the right thing to do.