Sure, if I carried around a privacy-centric Linux box and told my guest to use Tor browser, I could see how that could change the privacy picture. But that isn’t exactly an apples-to-apples comparison.
If you believe that having the guest user run their search on a typical Linux, Windows, or macOS machine would be better for their privacy, I would be interested to hear how.
Also, if they’re running the search in guest mode and they don’t log into a Google account, nobody can know who’s making the search. It’s not like they’re looking through the webcam or something.
> If you believe that having the guest user run their search on a typical Linux, Windows, or macOS machine would be better for their privacy, I would be interested to hear how.
The main reason is that Google controls the entire environment on a ChromeOS device (kernel, userland, browser), and ChromeOS is closed source so it's not possible for me to easily know what is going on. In addition, Google makes money by collecting data about users, so there is an incentive to collect as much information as they can get away with (and they've shown repeatedly in the past that they do just that). Maybe there's a daemon running in the background shipping URL history off to some Google endpoint in the name of "telemetry", or maybe not. Or maybe it's something more innocuous-sounding like hashed or anonymized data (which could be reconstructed given Google's immense amount of data). But I don't know, and I don't think it's reasonable for anyone to implicitly trust ChromeOS at all given the business model of the company that makes it.
On most Linux distributions, nearly everything is open source and I'm free to audit what's going on. On macOS devices, the software is closed source, but the company's business model does not involve building a dossier on each and every person on the planet, so I trust them more (not fully, but more). In the past I would have said the same about Windows, but lately I'm not so sure and I tend to put them in the same bucket as Google.
edit: Also see my reply to you in a different sub-thread where I explain this in terms of threat models. If you were building a secure OS to protect high-risk individuals like journalists reporting on intelligence leaks, you would be crazy to recommend that the journalists to use an OS built for them by the NSA, MI5, or FSB. Would you feel any better about the recommendation if the government agency said "Don't worry, as long as you use guest mode and don't sign in, we won't collect any data about you"?