I am behind so this may have been addressed...
We have used UR for rental cars multiple times and have never had a major problem. I do put a tiny bit of it on my CSR because I thought I read that was a good way to ensure that you would receive
travel insurance coverage if you needed it, but I honestly couldn't tell you myself if that is actually true or not. Might not make a different with the CSP or CIP anyway though.
I WILL say though, that we had to return a car a day early because we left VA early to fly west before the most recent hurricane hit. When we returned the car they told me the amount for the day we did not use it for would be refunded since it was a weather issue. I then followed up with Chase and they told me it would take a while but the points would be refunded. Most recently, we have received a message on our phone from someone from the rental agency telling us that they cannot refund it and we need to go through Priceline (rental period was just before they switched over to Expedia), Honestly, it was only the one day's worth of rental so not a lot of points - I just haven't had time to follow it up and quite frankly probably won't.
But it is just something to keep in mind - getting a refund if you need to return it early might be a bit more difficult than normal if it is rented using UR. Would this stop me from using UR to rent a car again? Absolutely not, but just thought it was worth mentioning since you asked.