If Chromebooks retail for $250 and have free-BIOSes ...

There are challenges in meeting the FSF's RYF criteria: https://fsf.org/ryf

Sure, someone could.
However, based on the wiki page, it seems that the freedom aspect of the Chromebook Pixel is questionable at this point.

The Acer looks nice, save Intel's binaries for the BIOS.
https://trisquel.info/en/forum/acer-c7-chromebook-updates
There's some valuable information on that post.

It's probably not possible at this time. There may be some potential candidates around the corner that it may be possible to totally free (at least the core board, ie not necessarily including hard drives, etc). There are issues with the wifi being integrated on most of the chromebooks. If you can't replace the wifi its a no-go as all the integrated chips (like ath6k) are dependent on non-free firmware. If we can find an upcoming model with a particular set of chipsets now shipping and also has a mini pcie half height slot (some do) then it might be possible to free one. These would potentially be better potential candidates I feel than other systems being worked on right now.

We've got an idea for another solution to the problem of a modern totally free laptop, but I'll refrain from going into detail right now. There are two entities I'm trying to get in touch with either of which could help us solve this problem. Basically the costs would be significantly less and price much more appealing. I can't see it being more than $500-600 USD at retail. At the same time though your not talking about something that would be competing with the power of a typical x86 system. However we're hoping the solution might be sufficiently powerful for basic computing tasks.