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According to Protected_Mode, to enter protected mode you use this assembly: Which I'm sure does work, but it seems like a strange way of doing it. I have fairly limited knowledge of nasm compared to - I assume - whoever wrote this code, but why do they first move cr0 to eax, then set the bit to say it's protected mode, and then move eax back into cr0?
I though - according to CR0 - that the cr0 register was read/write,

unlike the other that can be accessed only via the MOV instruction

Is there any reason why it's done this way?

You can’t perform ALU operations on control registers directly. There are no instructions for that. You can only move to and from them. Altering system registers is done rarely compared to general computational tasks. So, there’s no reason to penalize the latter by making longer ALU instructions just to make them able to operate on more registers. See, every register is encoded by its number in an instruction. The more registers you allow in an instruction, the more bits are needed to encode each register by its number. Longer instructions need more memory and specifically larger instruction caches. You should also keep in mind that the 80386 control registers appeared several years after the 8086/8088 ALU instructions and the control registers couldn’t be incorporated into the already fixed ALU instructions. They could be extended by way of instruction prefixes, but it would increase complexity without much gain.

The reason the control register is read first, is that is the only way of only setting bit 0 or any bit for that matter without altering the rest. Otherwise, if you did something like; then any of the other bits that are writable would be set to zero.