Yeah, I don't know, I don't see how you can't pause execution and store the entire interpreter state and DOM somewhere. Maybe it's just that nobody cares enough to go through all the effort?
Modern pages would also likely be much more touchy about the imperfections of such a mechanism. A lot of “old browsers good” in general seems to be about modern webdev, not modern browsers[1].
[1] https://twitter.com/awesomekling/status/2001483275546825079