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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.People just don't want to invest/search for random new games on random websites.
For games people want to play, and already have heard about, it wouldn't matter if they are on a website or a "trusted store". If Fortnite was made available to play only from a website starting tomorrow nobody would have a problem using it from https://www.fortnite.com as opposed to Epic's game platform.
And for games sold by big companies, it also wouldn't matter. It's about trust (which Valve or Epic has), not about web vs a launcher/store.
If devs can get that trust, then getting users to play the game on the web is not a problem.
>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.
You also need to download/cache that 1GB or 10GB if you use Valve or whatever.
As for caching it client side in the browser, you can do it as well, either as browser cache (browser vendors will just add the technologies for that), or as locally downloaded assets with direct access granted from the browser (the article already talks about using a new API for mmapping-style access to files outside the browser).