The bad news is that it's not the tech that is holding back web based game dev. It's the users. Market research and testing has shown that users dislike "just playing" a game in the browser. This is particularly true in the AAA segment that webassembly and its perf gains would best serve.
Players who play the high profile games that web assembly would allow you to make games for (think Fortnite, CS:GO, etc) all want to play games from a trusted download from a trusted store, not some random website. Please note, random is used very loosely here to mean "any store/website that isn't Apple Store, Play Store, Xbox Live, PSN, or Steam".
I foresee that we'll need some major player with a big game like Fortnite, Roblox or Mojang to spearhead using web deployed games before we'll see anything happen in this space. The existing "install to disk and play" is working just fine and game devs don't really see any reason to change that.
The other major thing is that most "slightly" big games (even smaller mobile ones) have assets in the minimum size of 4-10 GB of data. Even if you can render the game in browser, you have to download those assets. Yes, of course you can "load only what you need" but for many many games (source: my wife is a game designer and I'm a game programmer/web dev) that still entails at least 1 GB of data that would need to be loaded and is difficult to cache client side in the browser.