>Am I the only one who is afraid we are just going to turn the browser into a delivery mechanism for a bunch of fat-apps

If by "just" you mean "exclusively," then no.

I would be willing to bet that the vast majority of content on the web even today isn't "webapps" but basic HTML, maybe with some JQuery or Google analytics somewhere, but more or less still just documents. Webassembly augments what can be done in the browser, but it still serves a niche set of use-cases when the whole web is considered.

Until the day comes when you can't publish anything to the web without a compiler toolchain then I wouldn't worry.