I'm not sure quite what I'd call it, in terms of pithy phrases. Perhaps someone else can come up with something better, but my first stab would be "awesomeness aversion." There's a pattern I've seen, one that seems to be a creeping issue that even Gygax himself encouraged with some of his writing (despite at the table apparently being the exact opposite): the reluctance on the part of designers and DMs to just allow players to do crazy impressive things.
I think awesomeness aversion is not jest an apt phrase, it's plenty pithy, as well! Plus bonus points for alliteration.
I would slightly cabin it into different areas, however.
First, there is the "Five miles, uphill, both ways," issue- which you identify as the aversion to (inter alia) new races (Dragonborn, etc.). I think that this comes from a misunderstanding and glorification of the past- which is not just something that occurs in D&D. What you often see is the following:
Younger gamers don't fully understand how
weird early D&D was, and so they attribute some sort of "Everyone just played it like Lord of the Rings, but less fun" veneer to D&D- not seeing it for the very weird amalgamation of Swords & Sorcery, Science Fiction, Horror Movies, Westerns, and all sorts of other bizarre influences (even Japanese Kaiju Toys) that it really was.
Older gamers reach into the past and nostalgia, and often (instead of embracing the messiness), try to present a single unified version of what D&D "was," which is just not true. The past is never a monolith. Not to mention there is this weird reactionary impulse as you age- it's the same thing that makes people say, "My kids can't do X, Y, and Z" while conveniently forgetting what they did when they were that age.
So when it comes to issues like races, I'm not sure it's an
aversion to awesomeness, as much as a variant of "Yelling at clouds."
Now, there might be valid reasons for excluding races (lineages, ancestries) generally from a curated setting (or adding them), and I am always in favor of nuking elves from high orbit, but D&D has a long history, from the very beginning, of non-standard races. If you doubt that, ask Sir Fang.
Where I think
awesomeness aversion comes in (and what the phrase evokes for me) is when a DM is afraid of making a ruling because it is awesome. It's the counterpoint to the so-called "Rule of Cool." It's when a player proposes something that is outside of the defined skills or abilities and the DM just reflexively wants to say no, because the DM is afraid of allowing things that are "awesome" that are outside of granted/enumerated abilities. Because if they do, who knows where it will stop? It's a pernicious bugbear that many DMs have in their mind- "If I allow Player X to do this awesome thing, how can I
stop Player Y from
demanding to do the an even awesomer thing?" Unfortunately, when a DM is in this mindset, it squelches the creativity of the players.
We often talk about trust- especially how some games are "high trust" (in that the players have to trust the DM to make fair rulings). The flip side that we rarely mention, and what I think awesomeness aversion speaks to, is that "high trust" settings also require the DMs to trust the players. That the players are playing to the fiction, and not just looking for a loophole (which ends up in adversarial play, which is fun for no one).