Because it still has the same essential nature?
"Diegetic" in its usual usage refers, generally, to music or other features of filmmaking (and, implicitly, other similar mediums, such as video games), where music makes a huge difference for audience experience, but does not typically exist as part of the world being depicted. That is non-diegetic music. It could also be other things though. IIRC, Space Balls makes a joke out of the title crawl, by having it be actual objects floating in space? If not there, I'm sure somebody has made that joke before. Diegetic elements can be used seriously or for laughs; the former as an attempt to integrate the film(/VG/whatever) experience together, the latter to call attention to an incongruity we usually gloss over.
I think video games give us some very useful tools for this purpose. As noted previously, "menu screen" is very clearly a mechanic of a video game. The vast, vast majority of video game menu screens are entirely non-diegetic. They may, like in Ocarina of Time, feature contents which are physically objects in the world--Link's various boots and weapons and outfits etc.--but in almost all cases a menu screen is not something any character actually sees or interacts with. Some games even have to kind of break the fourth wall when explaining their own controls, where characters in the world literally instruct the player which buttons to press.
But in some sci-fi games, such as the aforementioned Deus Ex, it is actually possible for some menu screens to be truly diegetic. When JC Denton logs into, or hacks into, a personal or security computer, or uses a keypad, or various other things, we can see that he is seeing the same screen we are seeing. There is a direct, in-world correspondence between what the character experiences and what the player experiences. It isn't that this menu screen is merely representing what JC is seeing; it's that it actually IS what JC is seeing, just rendered for our eyes. Newer games may even make a little flourish of zooming in on the rendered computer screen or keypad, directly showing how the thing you're looking at literally IS part of the world, not just an external-to-the-story interface to make the gameplay simpler or more enjoyable or easier to code or whatever.
Since it seems to me quite easy to identify what a "diegetic" mechanic is in a video game, we can apply the same concept to a tabletop game. It'll probably need to be made slightly abstract, since video games are in general much more concrete than tabletop games (with the main exception of props, such as maps-and-minis), but I don't see why the general principle wouldn't transfer over quite easily.
So, it's not enough for a mechanic to be merely representative. Nearly all mechanics are that. It's also not enough for the GM to simply give an explanation for it--that, as stated, leaves the door wide open to declaring functionally everything to be "diegetic", rendering the term pretty useless. So that's a lower bound; we know we need more than just "the mechanic represents something" and "the GM can give an explanation within the world". And from our previous discussions, we have an upper bound on what's required: it can't be the case that any form of GM participation in the determination rules out being diegetic, because then almost nothing ever can be so.
Somewhere between the excess of "you chose something with GM preference! Not diegetic! Not diegetic!!!" and "Well, it's diegetic because I said so, and spent 30 seconds coming up with an explanation that ad hoc fixed all the holes that this might cause", there seems to be space for a reasonable standard. I don't quite know what it is yet, but we can use that "menu screen" concept as a guidepost, at the very least.
I think a good example of examining whether mechanics are diegetic is to look at how healing is handled. Do characters know that their world operates on hit points? In most contexts, they do not. People sustain lingering injuries. People slowly become less effective as they get more injured ("death spiral", which we usually avoid because it's very, very rarely entertaining, despite being a better simulation of injury). People don't stay at peak effectiveness until they then go completely incapable (or even outright unconscious), and people don't instantly regain consciousness after getting just a teeny boost. Etc. But some contexts might make hit points completely diegetic; characters know that their world works that way, they speak of "regaining hitpoints" (or whatever diegetic term is used), they understand that the only hit point that matters is the last one, they make plans based on these considerations, etc.
Conversely, a mechanic which is almost always sort of...soft-diegetic? Like it's understood that people in the world would know something of it, but it's rarely addressed and generally kept very very soft-touch. That would be spell levels. Wizards almost certainly understand something about how there are greater and lesser degrees of power (certainly, at least cantrips are known to be different from other spells). They know that they have access to a more-limited number of these spells, that they can only be accessed by those with a lot of experience, that scrolls cost more to purchase or even to create (and, IIRC, higher-level spells are also longer, requiring more page space, at least in 3rd edition, not sure about 5e.) So...this clearly has substantial impacts on the world, measurable ones even (the prices of goods), but it's also got lots of rules and specifics that might not actually be known or thought of that way within the world. Hence, while it almost surely is diegetic, it's implemented in a pretty soft way.
As I hope I've demonstrated, making a mechanic diegetic usually requires more than just a fiat declaration. It requires considering how people do, or at least could, think about their world. It requires integrating the mechanic into the logic and processes of the world. Perhaps it is a rare thing (my previously cited "you stabbed that goblin priest, he should be dead, but somehow he's not, and instead hulks out!!!"), or a thing that requires specific triggers, or a thing that only some people can do, or...etc. Such a thing rises well above the rather, well, simplistic implementation rules you've described like "Don't Make Contradictions" or "Only Use Diegetic Inputs". It requires a degree of, I guess, holistic implementation. You have to make it "diegetical" in a relatively expansive way, not in a tiny thin slice.
