The point was, someone being real real persnickety about "absolutely NO dragonborn!!!" isn't just excluding some weird hyperspecific interest. They're excluding a large chunk of players--who have been used to seeing dragonborn for at least a decade. Seems like an unwise move, if it's being made for light and transient reasons--and if it isn't, it seems weird that they would bristle at needing to explain themselves, rather than, as Lanefan explicitly put it, deciding to "pull rank" at the first sign of disagreement.
Perhaps let me rephrase. Consider a setting that has, say, no elves, the most popular non-human race. (I'm aware official such settings exist. Assume this is homebrew, and recently-created, at least compared to when 5e came out.) Don't you think someone who did that would be pretty likely to expect pushback from their players? That they'd need to, I dunno, actually convince them that the exclusion was warranted and appropriate, given the immense popularity of that option?
Why doesn't that apply to dragonborn? Why is it that one gets to be the whipping-post (well, them or tieflings, who have been around even longer!), the one everyone is like "this should obviously be a trivial exclusion"?
"They're old" is a pretty lame excuse. Tieflings have now been a D&D thing for longer than the time before tieflings. Dragonborn are getting close; they first appeared as "Dragonborn of Bahamut" (and "Dragonspawn of Tiamat") in Races of the Dragon, a 2006 book. "They're common" is simply the previous thing restated; prior to Tolkien, "elves" were primarily little cutesy sprites (hence why the Keeblers are "elves" rather than gnomes or whatever).
So why is it excluding elves either never comes up, or gets the expectation that a GM is gonna have to work to sell their players on it? It's gonna be almost as much of an ask as dragonborn--because both are quite popular--and history/establishment is no longer a particularly functional excuse. What gives?