It's true, there aren't any that I've seen that are more turnkey, but that's not self hosting.
I'm thinking something like Medium, where you enter your name/contact info etc... on one page and a CC and that's it.
A back end process registers the URL/whois, sets up a cloud host account, pushes a default package to the host (maybe even WP), then sends your email the key/login for the front end and the cloud host login.
So it's a one page setup for something that you can either use as a default Medium like site or SSH into and do whatever you want. You pay the monthly EC2 account, a yearly maintenance with a DNS Registry etc... like you would had you set everything up individually.
The only thing you can't currently automate is setting up people's accounts on cloud providers. I don't see that changing but would be interesting if you could.