More money may help entice more time to be taken from some of those other things, but some of those are more or less fixed (job, chores), not sustainable to give up for long (sleep, relaxing) or simply not worth a small (or any) amount of money to give up (family).
Enough money and stability that someone can give up their day job -- that's a different story. But that's a very big jump, and suddenly even $400k doesn't really go that far, assuming you can even get that money. There's a reason very few open source projects have a full-time developer being compensated by the community.
ChromeOS uses the Linux kernel.
Students getting Chromebooks aren't sucked into the Linux ecosystem and open source community that encourages you to improve parts of the system yourself. Instead, it leaves system maintenance (and learning experience) entirely to the administrator and really only provides Chrome as the operating system, with all implications.
Control your data locally? Why not upload it to Google Drive instead. Learn git commands? Better find that hidden Developer Mode switch, because crosh isn't going to get you very far. Get involved in improving Linux or Chromium? Nah, better edit some JavaScript in a web view with someone else's proprietary online code editor.
Google can (and will) swap Linux out of Chromium whenever they want to, because none of the interfaces and none of the community overlap. When Fuchsia gets swapped in, neither you nor the students will notice, and it won't have made a difference other than Linux having helped Google's locked-down, centrally controlled platform to succeed.
Either way, ChromeOS doesn't contribute to taking (co-)ownership of any of the above and encouraging the freedoms commonly associated with the use of Linux. Neither does it sustainably establish even the Linux kernel as pillar of the OS, it's just an implementation detail to be hidden and potentially replaced later. So why exactly should we look at ChromeOS as GNU/Linux having taken off for the casual user?
Also, $400k is, like, nothing in developer time (compared to what Adobe puts into their software, at least).