> What's the chance this is also due to less limitations in the hardware, rather than C compiler achieving "parity" ?

I'd say it's pretty small :). There's this quasi-mythical image of assembly language being used for clever optimizations and resources-constrained code by grey-bearded programmers but it's not entirely accurate. It's true that, since they try to

The video glosses a bit over the details of the timeling but most bootloaders I've seen after 1998 or so are definitely written in C, save for the early stages which are ASM largely because they're very CPU-specific and there's no reasonable way to go around that (i.e. they largely consist of stuff like "set bit X of register Y" and "load the address of Z in register W" -- all of which signal the CPU to switch into some particular mode, or tell it where a region of memory with some specific meaning is).

Prior to that it was more or less a combination mistrust in C compilers, assembly language being pretty common, and hardware and prevailing standards limitations, more or less in that order (the first two might be reversed depending on who you ask). For example, when it comes to bootloaders, it used to be that the MBR reserved only 512 bytes for the boot code (it used to be called "the boot sector"). 512 bytes used to be enough if what you wanted to boot was PC DOS 3.0, but definitely not for much else.

That was solved pretty quickly though -- albeit through a pretty convoluted scheme where the boot sector would contain only a small piece of code (the stage 1 loader) which prepped the system for, and loaded, subsequent stages, all the way to a full-blown boot prompt with menus and graphics and whatnot. It involved all sorts of trickery, too: you had to switch the CPU to the right mode (not a problem on most CPU architectures but a bit of a problem on x86), handle all sorts of crazy complications (remember logical partitions?) and so on.

A 386 would have been absolutely sufficient for all this, so the tech to do it existed all the way back in 1985. But for a long time, a lot of this floated around in assembly form in technical manuals and over various bulletin boards, so that's how people learned about it. Assembly language was common, there were good, free assemblers around (good and modestly-priced or easy-to-pirate C compilers would be available for DOS starting with the late 1980s, but the world didn't really get access to a good C compiler for free until gcc became popular) and a lot of this was intimately tied to the CPU anyway, so assembly was pretty much a natural choice. There wasn't much of a need for more complex bootloader code, either. With most hard drives in x86 computers in the tens of megabytes region, there was rarely much of a reason to do fancy things in the bootloader, either.

With BIOS and firmware it's a slightly different story. This was code that not only had to fit in a small amount of ROM (less of a problem than you'd think with C), but was also very CPU-specific, ran in a restricted environment (no RAM in some places, for example), and it's code that has a very long history behind it. I kindda lost touch with this field in the last couple of years, but back in the 00s, the codebase in a lot of BIOS ROMs dated back to the 1980s -- updated, of course, but the "initial commit" was in the 1980s. It had been through audits and certifications and long bug fixing sessions (some less efficient that others, one might argue). For a long time, big providers didn't see any reason to rewrite any of this in C. Sometimes they'd license it to other companies (some of them pretty big) that did wish it would have been easier to customize it (and often screwed up customizations) but life was what it was.

They did eventually move to "assembly with a sprinkling of C", but in principle, they could have done that as early as, what, 1992? I've definitely seen firmware code from that era written in C and ASM. But let's call it 1996 to be a bit conservative. Definitely 1998. But a lot of companies didn't move to that until way later, because there's a sort of caution (or inertia, depending on how you look at it) that being responsible for a high-volume product that sells millions upon millions of copies tends to impart. Or at least it did back then, when firmware updates were difficult to deliver.

There are some hardware limitations that do play a role in this. For example, early stages of firmware code run without RAM, so they run without a stack, which makes C a no-go (I dimly recall a C compiler that offered very limited support for that kind of environment, but not without a lot of hand-holding with macros and it was bad to the point of uselessness).

But by and large, that's not what held people back. If you work with a good compiler and understand what's behind the scenes (not a big problem if you stick to readable C without clever tricks), having just 8K of ROM and 512 bytes of RAM isn't necessarily so constricting that you just can't live without assembly language. I've seen (and written) non-trivial firmware code in C that did a lot of stuff in that kind of space.

Edit: if you're good with assembly, and trade the problem-space knowledge that you (unlike a compiler) have, you can write less general code than that which the compiler generates, and generally beat it in terms of size. So you can squeeze in more stuff in X amount of code than a compiler could. Whether or not you want to do that is another story. With firmware code, yeah, maybe, at least back when having 256K non-volatile memory was a significant hog on the motherboard price at high production volumes. Nowadays I'm pretty sure the answer's no (but I haven't written firmware code for that kind of hardware so take it with a grain of salt). With bootloaders I'm pretty sure the answer has been no for more than 20 years now :).