I think of good applications as a collection of SPAs. There is no benefit to forcing every single feature of an app into only one page. Ajax means we can implement more functionality without a page reload, which is good to a degree, but at a cost of slower initial load, losing URL state, and difficulty tracing UI behavior to underlying code.
I am working on a legacy SPA now and it's horrible. (Our users have learned to refresh frequently due to uncertainty of state.) I am not sure how much to blame on poor implementation as opposed to inherent weaknesses of SPA architecture.
Almost all of the SPA frameworks out there right now are nightmarish. I think React is pretty good but limited. What you're describing is probably a much better way to handle the needs of most sites.
I am working on a legacy SPA now and it's horrible. (Our users have learned to refresh frequently due to uncertainty of state.) I am not sure how much to blame on poor implementation as opposed to inherent weaknesses of SPA architecture.