The problem with the question is that it’s based on the assumption that TAS was not considered canon because it was unavailable, which is in error. TAS was decanonised in fandom’s minds only because Roddenberry decided he didn’t want to consider it canon, not because nobody was watching it.

Ultimately, Roddenberry’s stance on continuity was that it was whatever he wanted it to be, whether it was broadcast or not. Richard Arnold famously noted that Roddenberry would even decide that he no longer considered bits of TOS canon, and that his stance on what was canon and what was not even changed from day to day, but by that time Gene wasn’t in charge anymore.

Star Trek is replete with contradictions and inconsistencies, and we of course it’s fun to play the game where we try our best to reconcile these inconsistencies with continuity, logic twisting, speculating on things to fill in the gaps. It’s the same game Sherlockians have played for generations (hence Watsonian and Doylist explanations).

But it’s only fun until we reach the point where there’s really no explanation satisfactory, so we then stop and quietly exile that point, pretending it doesn’t exist. And that’s just in the broadcast media. When we add in the tons of licensed and unlicensed fiction, it just becomes overwhelming to juggle.

But here’s the ugly, unspoken truth. I once formulated this rule a long time ago for Doctor Who, which has an even looser relationship with continuity and a more massive body of licensed work, and worse still has time travel and history changing baked into its very premise: “It’s all canon. It’s all non-canon.” Canon is whatever whoever writes it wants it to be. Nobody’s there to really stop them, and any adherence to continuity in fiction is a choice, not a necessity.

You don’t get to define canon. I don’t get to define canon. We don’t even get to define canon for each other. All we can do is define a basis for discussions to take place. It’s so easy for you to assert something and me to shoot it down by saying, “oh, that’s not canon,” without addressing the meat of the argument itself - not whether something is canon or not, but whether that something actually makes sense. And that kind of impasse becomes infinitely more impassable if we don’t have a standard definition of canon to begin with.

So questions like, “Is Prodigy still canon,” are ultimately non-productive (and a classic closed question) because the answer really is, “It’s canon until someone who has the authority and the ability to say otherwise says so, and even then.”

And we can pile qualification upon qualification upon this kind of definition until we miss the forest for the ever-expanding numbers of trees, when in the end Star Trek is fiction, fiction is malleable, and the hallucination can only be shared if we share common ground as to what exactly the hallucination is.

So it’s not availability rules, it’s not Roddenbery rules, it’s simply the agreed on rules of engagement that canon is whatever’s been broadcast by the main rights holders. Discussion is only productive if we agree on a foundation like this. Otherwise it dissolves into headcanons and no one is more valid than the other. So the conversation trundles to an awkward halt (and sometimes name-calling) as we hug our individual ideas of what constitutes canon and refuse to accept anything otherwise. It’s a fun-killer.

And that’s why we really shouldn’t quibble about canon.