You write this as if a "webpage" is one single thing. Maybe you picture a simple news article or blog entry - sure, it's fundamentally a document, HTML is almost purpose-built for publishing that kind of content.
On the other hand, there are countless webapps that are being built to replace what used to be (or would normally have been written as) desktop applications. The document model is poor fit for these. SPAs deliver a better, application-like experience.
These two things can coexist on the web. It doesn't have to be all one or the other. Flutter obviously targets the app experience, and you'd be foolish to use it to target the document experience. You'd be just as foolish to go the other way; page-oriented admin UIs (example: Shopify) are awful.