I haven't really understood whether firmware level infection (on either motherboard or drives) can actually be a thing without physical access
It's possible because you can update the firmware on many boards without actually needing physical access. The common case is to use the EFI Capsule Loader interface, but there are other methods out there too, one of the scariest being the use of Intel AMT to reflash firmware remotely with zero interaction from the user (there are actually systems that can do this).
however how can one factory reset the firmware in that case?
Any method of doing it with the system powered up requires cooperation from the firmware itself, and it's pretty trivial for the malware to just not cooperate (in fact, it's actually easier for them to not cooperate than it would be for them to cooperate). As a result, you need to physically remove the flash memory chip that contains the firmware, and then manually reprogram it using specialized hardware (well, specialized from a typical end-user perspective, you can use pretty much any SPI flash programer you want as long as it has the right interface). DOing that is going to be functionally impossible for most people, mostly because it's nearly impossible to get the raw firmware image out of the update packages from the vendor (the hardware to actually program it is cheap, and it's not something that takes more than some really basic skills to use).
Is there, in particular, a way to be sure it was reset to a clean version, without interference from a malicious edited firmware?
Verifying the firmware image you're going to use is sufficient, provided you actually reprogram it correctly.
Do motherboards have some sort of uneditable, ROM-stored version you can fall back to?
As a general rule, no, it would be wasted space and power for 99.9% of end users, and would also be a logistical nightmare for the support staff.
Many good motherboards do, however, use transactional updates and have a backup copy of the firmware (it starts as the same version, and then after the first firmware update it tracks the last used version. This doesn't really help though because anything that can rewrite one can just rewrite both.
It seems so lame if editable firmwares in motherboard simply created new security risks...
Updatable firmware is not something new. The concept has been around for far longer than most people realized (the oldest PC's I've seen that could do it without needing programming hardware or a manual chip swap are from over a decade ago). It's only recently that it's become really widespread though because UEFI makes it much easier for the OEM to provide support for it.