That's what I liked about Koizumi and Miyamoto with OoT. They had no clue what they were doing. Koizumi ended up doing all the character modeling and animation for Link, simply because no one else really knew how to do 3D. And the guy was like...20 years old at the time. They all just threw stuff together and it ended up being really really special.
That was really an extraordinary situation to be in, not unlike to when Miyamoto started as a game designer prior to said job description existing... A few years before, hence he had to do everything, programming, graphics, music before he gradually was relieved of said duties.
By the time 3D came everything had fell into place for 2D, but clearly hadn't set in for 3D because very few people were trained for it and there were no tools whatsoever, Koizumi doing 3D didn't happen by mistake, he entered Nintendo as a script writer, I think, but he continually tried to make the jump to other areas of development (he wasn't settling into one speciality) to the point of getting involved on a Zelda II poligonal remake on the SNES (using the Super FX chip, I think).
Game wasn't polygonal 3D per see, but it was all about animating poligons (read vertices) instead of sprites. I think "Another World" graphics must have been the goal. Still, you were animating polygons, it's one coordinate less from 3D, from them on he was on track to be hand picked for whatever project with polygons arised.
Anyway, Ocarina of Time was the second time Koizumi did something like that, as he was credited as a 3D Animator for Mario 64, interestingly enough though,
he wasn't the only one as Satoru Takizawa is also featured in the same category. And if we delve deeper, we'll realize Giles Goddard also did some, for Mario's face as well as the whole "dynamic vertex" calculations, these games in the beggining were really group efforts, potentially everyone did a piece of everyones work, or worked on systems to make it a reality.
Not to say he was a 3D artist, but...
Nintendo had motion capture down at this point, just think how grueling and horrible these games animations would be otherwise.
Koizumi was pretty much a 3D artist at this point, but you can't forget that Ocarina of Time had pretty extensive Motion Capture, with even actors being hired for it. Mario 64 was more homely so they probably did it themselves, but you get my rift.
Him ending up on the Super Mario 64 team doing 3D animation wasn't surprising, and it was as much as he didn't new what he was doing as it was that there weren't enough tools to make it go smoother.
Anyway, he was far from the only person contributing to the project there, OoT even had a cutscene team.
And then you have some guy that deserves to be mentioned more than he usually is; Takumi Kawagoe, he was responsible for Starfox 2 programming (if you ever play it you'll realize everything needed to develop both Mario and Zelda is there, camera, even lock-on in third person view - and it was cancelled due to this Nintendo wanted a leap, not achieve what they were aiming for on the N64... On the SNES), this means Mario 64 was this guy's second 3D game, and Zelda OoT was his third (for which he developed the cutscene changing equipment tools and stuff like that).
In lots of ways, Starfox 2 was patient 0 for Nintendo, just never released officially.
Even in Mario Galaxy you have Koizumi sneaking into the office at night and adding special gems into the game. Or the guy who secretly put a fishing minigame into OoT while no one else was paying attention.
Same guy who did the same for Link's Awakening.
These people weren't working because it was their job. It feels like they just really really wanted to make something that was important to them.
At this point it was certainly more than a job, they saw this as the future of videogame development, so getting a development time extension to perfect something they were in the middle of doing/perfecting meant a lot for them. There were seasoned video game developers who suddenly had a new reality going on, they were adapting as fast as they could, any pretence was good (and they were seeing painstaking results coming out of their sweat and tears).
It's like when you start doing something and want to master it, really. There was the Nintendo way of doing things helping, but above all they were very motivated in mastering it. They felt it was very important.
But that doesn't detract from your point at all.
EDIT: Backtracking a bit, I think one of the issues these days, and going back to your cooking example, is that people are too comfortable in being one trick ponies, like... These days you study to be a freaking videogame designer. That's like studying to be a director or simply "boss" for Christ's sake.
That's like being the pastry chef. Do me an omelette. Oh no sir, I don't know how to.
Whaaaat?
You do 3D modelling, you don't know anything about programming and realworld limitations - you work with specs, that means you either play it safe and nobody complains about your average work EVER, or you try to push limits and people keep coming back to you because you broke something on their program. It's not a joint effort, it's bashing heads.
You do directing but you know nothing about doing the other guys work, hence a guy tells you he's been really busy animating a ball and you believe it. You get what I'm saying, I'm sure.
How do you expect a guy who directs you to... direct you, if he thinks the work you do is pretty much sprinkling fairy dust on some shit and voilá? You don't, guy's not directing you, he's blindfolded or worse yet, he hasn't learned how to see.
The reason Miyamoto is so good, or Koizumi, is not because they have vision and are intelligent - that's a big part of it, yes, but they know the basics for everything, you can't just say "no, that won't do", it's the same for Iwata, dude was a proliferate programmer, just because he doesn't program now you can't exactly fool him easily on a tech explanation you're pulling out of your own ass to save your hide.
That creates tons of wasted work or lots of bottlenecks all this talk about "oh, it's so powerful I don't have limitations as an artist" we hear sometimes is just a pile of shit because you always have limitations and always will, the fact you can do it more sloppily now just means framerate will take a hit or the game will have less stuff going on than it could have otherwise, it's that simple.
I'm a designer, looking for a job - and the other day a programmer guy that knows me was telling me "hey, if you were applying for web design you would be employed and earning way more than the jobs you're applying for as of now" so I explained to him why I didn't do it/like it and he was like "oh, you understand this shit so much better than everyone I work with and it's as you say, that creates lots of wasted work because people don't see eye to eye"
Dudes don't understand the reason for their creative "canvas" limitations. I understand them and understand that's not my strong suit (against areas I've constantly honed) because I don't know how to do the programming part (or rather, learned it before, hated it, forgot it, learned it again, 3 times) so I don't do it. You have to understand what the fuck you're doing or you'll just be average - and average is what the guys he mentioned are, they're also incompetent in my book if that state of affairs is more than passing and they'll be doing that for long.
If I apply for that kind of job I'll just re-learn programming because I'm competent at least to be able to do something on the programmer day off or debug myself everytime something goes wrong, and I'll feel miserable and caged - but I'll be competent.
Lots of incompetent "one trick ponies" out there.
... I actually know a few in the videogame industry that worked for commercial games and my reaction is the same every time, how did this guy manage to work on said industry? I know good programmers and 3D modellers, simply specifically not them.