Is any restriction by the DM allowable in your opinion?
You did not ask me, but yes, plenty are.
But it's not a simple "oh yes that's always 100% safe" kind of thing. It's messy. Intent matters, for instance, and can go back a ways. Friendliness matters. If someone goes the extra mile and genuinely tries to make me happy, but despite that effort it just doesn't make sense and we have a long and positive conversation about
why it doesn't, then I might be inclined to accept even many restrictions I would find irksome in other contexts.
"No, you can't have dragonborn, I don't like them" or "It's world consistency, if you don't like that, I can replace you" are the exact antithesis of that. That's throwing your GM weight around, pulling rank, emphasizing just how far apart the GM thinks we are, looking down from their lofty perch.
Someone who earnestly works with me even if it doesn't end up working? They've done the work to earn my respect. I'm willing to work with that. Hussar did some of that when he offered me a place at his table.
Or must the DM always allow any and every idea a player has that is within the collective of a system's rules?
Well, just as a preliminary, I prefer a game designed sufficiently well such that splat options aren't any more nor less powerful than so-called "core" ones. So for a game I would consider well-designed, the "within the collective" part would be irrelevant. So, if it's a first party option, then I hold that if it's first-party, it's reasonable for the player to presume it's available unless, as noted above, the GM has done the work to get the player on board with less.
The human in the DM chair, do they have any power to cultivate a game without committing a red flag?
Curious little me wants to know
I don't know what specific things count as "cultivate a game" to you, so I am hesitant to agree without knowing. However, I can guess. As part of that, I again want to point out the extremization going on here. Notice how your argument (in Socratic question form) is built on the presupposition that the GM must be so horrifically constrained that you don't see how it could still be possible to "cultivate a campaign", and thus invite us to defeat ourselves by revealing just how horribly limiting we (surely!) must be.
I think I can safely assume that "cultivating" includes:
Drawing maps, local, regional, continental, perhaps global/planar
Preparing cultural, political, religious, and economic info about various places
Having a timeline, specific or loose, for recent and long-term historical events
Naming tons of things (nations, languages, rivers, cities, etc.)
Populating the world with NPCs of various sorts (antagonist, ally, competitor, bystander, shopkeep, etc.)
You may have further ideas along this same line, but I think I can stop there. None of the things I listed are prevented or even meaningfully impeded by the presence or absence of any specific D&D species. Nor would they be if we were considering class.
Backgrounds could perhaps be a problem if they are tied to something particularly specific and difficult to reflavor. Something like the Ravnica guilds or Strixhaven student ones, since those have some pretty specific flavor. But most backgrounds, especially if you use 5.5e only, would likewise have no impediment whatsoever on doing the above things.
So, now, if I may ask some Socratic questions of my own...
Is any player freedom allowable in your opinion? Or must the player always submit to whatever the GM says, no matter what? Why is an adjustment to help make your players more enthusiastic to play in your game antithetical to "curation"? How much control do you actually need to "curate" the campaign for the group? The human in the chair, do they have any ability to play what makes them genuinely enthusiastic without committing a red flag?
I have endeavored to match the congenial but clearly negative tone of the original questions, albeit including an extra question or two.