There were a few chromebooks that ran on ARM chips. Not sure about sturdy, but they were definitely cheap. (And, you can enable developer mode and then use whatever flavor of Linux you like.)

Also, the Microsoft Surface RT tablets were ARM and fairly impressive from a hardware standpoint (sturdy, nice screens, etc.) You should be able to get a used one on Swappa fairly cheep. I know there was some credential leak recently, but I'm not sure if that's gone far enough to make it a useful development machine. (Also, it's a tablet with a kickstand and a detachable keyboard...)

There's still a tranche of early 2015 Rockchip Chromebooks, already with Coreboot on them - and you can even put Libreboot on at least some of them:

https://libreboot.org/docs/install/c201.html

MIPS and ARM laptops exist, or an old Thinkpad X60 with coreboot.

I actually have an X60! But it's 32-bit x86, so these days it mostly collects dust while I use a Thinkpad X301.

Where does one find a MIPS or ARM laptop? Who manufactures them?

ARM laptops exist in the form of various chromebooks. No clue if completely free firmware exists for any of them though.

You would start to look at Novena, but that might not be quite the answer you're looking for.

Novena is great, but it certainly isn't cheap, isn't sturdy, and to be honest, unless you were lucky enough to snag a Senoko battery board, isn't a laptop. (I'm fortunate enough to own a few Novena boards).