I have a mains powered Karcher one that I bought for the car and motorbikes and still take the car to the car wash…
As above, there’s a lot of lugging around and plugging in hoses and then coiling them back up and unplugging everything etc. I sort of regret buying mine to be honest.
Have you had a look at the pump action ones you can get on Amazon? I used to have one when I lived in apartments in London with no access to outside taps. They look a bit like those weed killer bottles that gardeners carry round and you just fill it up, pump it a few times and you get enough pressure to spray. You wouldn’t want to regularly clean a car with one but to just wash off the screen/wheels as you say it might work ok.