EDIT: I tried to do just this, and both of them blocked it :(
Refused to display 'https://www.google.com/?q=cheese' in a frame because it set 'X-Frame-Options' to 'sameorigin'.
Refused to display 'https://duckduckgo.com/?q=cheese' in a frame because an ancestor violates the following Content Security Policy directive: "frame-ancestors 'self'".
Also FWIW, iframes can still be useful on the regular web for third-party widgets, as well as same-domain pages.
If the web is a 'turing complete platform', then it should be possible to run a web browser in a web browser. So Chrome inside Chrome. That could be anywhere between the level of 'webassembly to run the whole thing', or it could be at the level of 'iframes give all the necessary functionality'. Today the first isn't viable because webpages can't make raw TCP sockets. The latter isn't viable because of the way sites can differentiate between iframes and the top level window.
If I have to use a fork/modified copy of Chrome for the outer copy with slightly different rules, then it isn't capable of implementing itself.
Imagine if gcc couldn't compile gcc - you needed to use a seperate compiler-compiler. It's the same thing.