Having your stuff in it already, it's always available immediately (for you), not needing to worry as much about getting it dirty at the beach or with a dog, going to remote places where calling a Waymo may be infeasible or would take a really long time. Probably also cheaper if you drive really frequently.
I don't know you or your situation, but many people (including the idealized version of Rivian's target market) like going places that Waymo currently doesn't. There's also tradeoffs with cost, wait time, # of passengers, cargo, etc. Some people may also want to automate "boring" driving while still having the option to do "fun" driving
My cars are more than just transportation. They're mobile storage lockers where I can keep my stuff reasonably secure. They're a place to sit warm and dry while I wait for something else. They're (semi) private changing rooms where I can put on my cycling kit. Regardless of who does the driving I'll never give up owning (or at least leasing) my own private cars.
> pay for insurance, gas, tires, oil changes, parking, washing etc.
If you use a car you are paying for those costs. There is no getting around it. If you uber it is indirect, but part of your costs per ride is going to those things. Renting a car gets someone else to do them - but you are paying them to do that somehow. (self driving make trade parking for gas where parking is expensive, so in the densits areas this can make sense, but only because the car is driving empty out to the suburbs in the morning and empty back into the city in the evening - so it increases traffic)
If you own your car you can choose to not keep it clean. The rental will not allow that choice and so you pay for it.
It won't be much if any difference. Rush hour is when most people are trying to get around. Worse, they are all trying to get to the same place, so if you are thinking two trips downtown - that means there is an unoccupied trip back out to the suburbs every morning (and again in the evening) - perhaps more if we are also parking in the suburbs where parking is cheap (though this is probably offset by the cost of parking downtown)
This is better solved by leveraging more traditional forms of transportation. Making biking, walking, and various forms of transit easier, safer, and more effective. Cars, whether self-driving or not, are in direct opposition to this.
I'm sure they could be useful to folks that have the specific use-case for it, but the vast vast majority of trips in a person's day-to-day are better solved by robust multi-modal options and public transit. The benefit there is that less drivers means that traffic is actually better for everyone.
I actually see this as a benefit! Cars take up a lot of space and so now there exists massive right of ways that can be used and modified for other transit modes. Take a lane away from personal cars and dedicate it to buses so they can run faster and avoid traffic. Remove some street parking spots and create a protected bike lane or a street market or something else. The extra space can be a huge boon. It’s pavement, basically a blank canvas imo.