I've spent most of the last decade working on data-intensive web applications which definitely deserve to be SPAs. There's lots of opportunity, especially if you're willing to move away from the "retail" public-facing web.
What do you mean by data intensive? I'm thinking something that looks like a bloomberg terminal, complex tabular data or complex visualizations. Those are cases that should never be a web app at all, even with recent improvements HTML is a document format and horribly suited to those use cases.