The first case happens to me all the time. I dont know if it's iOS killing the Tesla app after a lengthy enough period of the car being asleep, or some other factor, but indeed sometimes the phone simply doesn't unlock the car without opening the app and letting it explicitly reconnect. Irritating, especially with hands full of grocery bags.
The third case has a workaround - there are Apple Watch apps that will take an auth token (easily obtainable) and both control the car and act as a key. I have not tried one, and they do recommend you have your card key just in case, but having it set up would help the stolen wallet & phone scenario.
I'd certainly rather have a fully-supported technology like CarKey that worked all the time. It'd be great if a U1-compatible hardware upgrade could be done at a service center for existing vehicles.