MS and Apple already have/will have/build ai features into the OS and intel is also adding AI cores to laptop CPUs. So when you have a webbrowser based photo editor or other tools, you can build things which do not require a backend server. Not everything has to run remote and without such an API you can't use it locally. Perhaps this will allow me/us to write a website for a local agent as well or an assitant.
The question is more boring than that. I agree that running models in the browser would be cool. The question is, where are the models coming from? If they're downloaded & stored for each website, that's going to get out of hand very quickly. It seems to make sense for browsers to ship with some useful default models, but that doesn't seem to be what the specification is for.
I would be happily running my custom agent models on my gpu without sharing those models and still being able to use the browser as an interface.