I'd say "it depends". Having a tiny laptop-type thermal solution (high TDP chip, low mass heatsink, tiny whiny fan) would indeed just be as annoying as a laptop, but there are plenty of configurations where it works just fine. The larger NUC-style devices (generally marketed as "this one has room for a 2.5" drive) with low power chips when used for light basic work don't really consume enough power to get hot.

This is even something you can make completely passive; check out some of those ODMs in China that make passively cooled M and U series Intel PCs. Generally marketed as industrial PCs and software routers, they do have 18W parts that work fine in 35°C ambient for years and have plenty of performance. It really depends on what you use it for. (Qotom is one of them, there are a lot of white-label manufacturers, but when they make the boards it's pretty close to the 'actual' ODM instead of just another re-badge)

Do any of those ODM boxes allow open firmware like coreboot? Protectli is one option, would be nice to have other choices.

Protectli is just a rebadged ODM box. Most of the boxes I've seen don't have BootGuard fused so you can run coreboot on it.

On the other hand, you can't run coreboot on most things, including the Gigabyte Brix Pro.

Any good search terms for those ODM vendors? e.g. I couldn't find much for a search about Qotom and BootGuard or coreboot.

There is one explicitly listed on the coreboot mailing list a few times. On the other hand, there aren't a whole lot of up-to-date coreboot setups for Intel anymore. For recent AMD platforms, there is none.

If you really want to use coreboot, your best bet is to first look up what platforms are supported (i.e. 6th generation Intel) and then look for an ODM that is making a 6th gen system. Next step is to simply ask if they fuse BootGuard or not, and if they do fuse it, how much of it. In many cases you can't run Coreboot in pure form anyway, some blobs will remain to get basic functionality working. If you want a deblobbed boot your options are practically restricted to very old platforms, or 2 or 3 commercial offerings.

Agreed, although it differs vastly between models, I'd say it's rather the opposite if you opt for passive 3d party heatsinks(chassis) which are plenty for Intel's NUC, even 80W TDP models (Iris Pro). Passive cooling for desktops is way more complicated. I've been using Akasa for my Skull canyon for years for my dead silent setup.

Akasa's fanless Intel NUC cases are excellent. Hopefully they will create a fanless case for Ryzen NUCs, or generalize an Intel fanless case to support multiple port layouts.

There are definitely computers between the Brix and a full tower. My old computer is a full tower but my new gaming rig is a mini-ITX build that takes very little space on my desk and I plan on replacing the full tower with something like a Mac Mini in the future.

I would love a small MicroATX case without support for DVD-RW or 3.5" drives. MicroATX is inexpensive and effective (cases usually support standard ATX power supplies and PCIe cards without a riser, it's easy to mount a full-size GPU and common heatsinks, etc), but it seems hard to go significantly smaller then my own case (cm 36x36x17). But there's a lot of empty space in the front, so it should be very easy to get the depth down to 25-26 centimeters or something like that.

But I couldn't find anything like that, either you get flatter, HTPC-like cases designed to stay horizontal, or cube cases (which aren't so nice IMHO, since they take more horizontal surface on the desktop), or you need to find a small mini ITX cases (which can get very small, but they may require SFX power supplies and can be harder to cool down).

A desktop is still a nice thing to have. They can be quiet even when the workload is consistently high.