Unfortunately, the web became the only app platform that was perceived as being politically neutral, and so there was huge pressure to add features to it. These features all hugely increased the complexity of HTML renderers, and with complexity came bugs.
Could you build a smaller, simpler, safer web? Sure. It's called HTML4.
The modern web platform's bloat and what you can achieve with it always reminds me of 1990s demo scene mags on floppy disks and their mag engines. I think most of the problems stem from adding more stuff to HTML rather than taking what we build today building the smallest possible DSL and its engine around it. At some point we have to do a cut like that or we'll have browsers that'll have to support many, many HTML profiles and become monstrosities.
As wasm defines a VM, the browser could become useless.