That's a bit oversimplified. I had this thought too and tried to figure out why this is different, and I think there are some major points. The biggest one is in which order they were built and designed. If we take Java and ask why applets didn't take off since they could do everything WASM offers and more, two things come to mind: it was fucking slow on contemporary machines, and the gui framework sucked. WASM is the complete opposite. The gui framework is HTML/CSS, which despite its idiocy in many places had a long time to mature and we've generally came to accept the way it works. Now we just tacked a powerful VM onto it so we don't need to target slow Javascript. There isn't even a new language to learn, just compile whatever you want to WASM, which means you can use a familiar and mature dev environment.

The other point is that WASM is way more open than any of the mentioned predecessors were. They were mostly proprietary crap by vendors who didn't give a shit (flash: security, Microsoft: other platforms) so inevitably someone else would throw their weight around (Apple) to kill them, and with good reason. WASM is part of the browser, so as a vendor you're actually in control regarding security and other things, and are not at the mercy of some lazy entity who doesn't give a damn because they think their product is irreplaceable.