So... no server-side rendering, no accessibility, no text selection, no "read me" or "read later" modes, no text field inegration for auto-fill, lack of support for classic navigation and bookmarking... and it's transpiled to JS, so plenty of language issues lying in wait there.
Plus I saw no mention of just how large the Flutter rendering and support libraries are (e.g. just how big is my Flutter web app?).
"About to win over?", hardly. "Could win over?, sure.
But more in the sense that ANYTHING could win over the web. Possible. No probable.