If you weren’t the fine upstanding person you are, you’d have all the web traffic of users at your disposal: banking, secure interactions with healthcare providers, credentials to Hacker News, the whole nine yards.
With access to my email, you could probably reset a handful of my passwords to various services that don’t support dual factor auth, and you could probably discover what services I subscribe to.
I mean, I wouldn’t want you to have access to my email, but I would much rather that than a permanent man-in-the-middle web client.
It should be quite doable to spin up a container/VM on demand. I'd probably look at lxd/lxc or bsd jails for this (both with zfs for storage) - or if there now are any real ways to run containers under hw virtualization - maybe that.
Now that you describe it, yes indeed I can see the problems. I can't think of any other precedent, as most other proxies are least protected by HTTPS, wheres a Browsh service is literally reading every character on a page in plain text! So there's need to be a great deal of trust. I wonder if it's just too much to ask of people, especially where money is involved.