Serious question: Why would it be preferable to have something like this in the browser? The thought of having to keep track of a browser tab that you might accidentally close and lose all your work doesn't sound great.
This is easy to fix with local storage. You reopen the tab and you're right where you left it. Unfortunately the companies see it as an opportunity to lock users in with cloud saving.
The allure is that the web is the most open, most stable and the most cross-device platform we have. Almost anything that was made for web still works today, with Flash and Java applets being the two big exceptions. Following the Lindy effect the self-contained web apps of today will still be operational far into the future.
Contrast this with Android's pathetic record of constantly breaking backward compatibility and restricting what software the users can even run on their devices.
I would like to see something like this in the Web simply to allow for collaboration.
I would love to see a DAW where randos upload just a track—maybe a drum track. Other's can "create a branch" where they jam along: add a bass track. And let the jamming, branching, songwriting commence.