If Chrome had installed 4GB for some other tooling that most people don't need, would anyone care? My operating system installs with a million default packages that I don't need. Users install applications with optional features all the time. Applications install additional tooling so that they'll function all the time.
To the other point: of course Claude Desktop modifies the browser--that's how it works. Most apps install integrations with existing apps. Often apps install a whole collection of plugins, even for things the user doesn't use, so they're available if the user does start using the other apps.
The fact that this happens to be AI-related is a moot point. The environment concern is utter nonsense. They're not using everyone's browser to power AI for others as some kind of shared collective resource. 4GB is not a lot of data in the grand scheme of things (beyond general application bloat). I have more than 4GB worth of ads shoved in my face every month.
The legal argument is facile as well. When you install any application, its terms of service cover functional updates and additions. You don't have to explicitly consent to all of them.
Other than the size of it, I don't have any problem with anything this article is mentioning.
This is a huge nothingburger that only caught peoples' attention because of the irrelevant mention of AI.