Browser vendors agreed that they could standardise something lower level than JavaScript, in the browser, and is is the chosen outcome. Why _not_ make something new? There is experience doing it, so it's possible, is a known engineering task, and it can be built to the specific requirements. And by making a new one, you don't have to buy into someone else's brand or ecosystem.
The rest is historical details.
Ultimately, asking strangers on the internet to justify software architecture design decisions that happened years ago and worked out rather well, is for the birds.
In future the question is going to be less "why use WASM when JVM is right there, one install away", and more "why use JVM when WASM is right there, zero installs away" .
those properties are important