What we need is VPB. Virtual Private Browser like VPNs. Essentially standardised cloud browsers that can execute your requests and send you back the result as bitmap buffers.
Not all websites work well, and you get a lot of captchas last time I tried it. From memory the way they make this work is pretty cool though, they capture Skia draw commands and send those over the network and use a wasm library to replay them.
Great idea! How to make sure that the users data stays private without the cloud knowing where the user is surfing. And I wonder how to monetise it? Subscription?