The fear isn't that it requires that. The fear is that it enables that.
The web is, and has been over the past two decades, in the constant state of war over control between publishers and consumers. People - and especially businesses - making pages would like to have 100% control over how the webpage/app looks and is being used. But the users would like to have some control over what they're viewing too[0].
The most widely known battle in this war is the battle for ad-blocking. The publishers want you to view lots of ads. You want just the content, without any of the ads. So far, the technology (and economics) favors the user, but it's not a given.
The balance of control on the web was always maintained by the technologies on which the web standardized on. Pure HTML, or even HTML+CSS, strongly favours the user. JavaScript tilts the balance significantly towards the publishers, as now they can (and do) generate content with code, which renders the page difficult to interpret and modify on the user end. One of the biggest complaints about Flash was how shitty the pure-Flash/mostly-Flash webpages were. That's not an intrinsic problem of Flash - this happened, because Flash gave the publishers too much control. And publishers (again, especially businesses) will use (and abuse) any control they're given.
The fear here is, that WASM against tilts the control in favour of publishing, which will lead to abuse and web becoming a much worse place for the consumers. If WASM will, by virtue of efficiency, enable publishers to embed a browser they control within the page, the publishers will use this, because this would single-handedly eliminate most ad-blocking, userscripting and scrapping efforts.
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[0] - and the power users, like myself, would like to have 100% of that control - think of how much better the web would be if the data was always published in machine-readable format, without tons of bullshit paginations and stylistic choices to scroll and click through. For instance, when looking for current weather, I want to input my location and a time span, and get weather data. I want to be able to script that. I don't want to waste time looking at ads, pretty pictures, non-relevant text and links.