Kinda sorta. Those limits are placed within the writeup of the game. It's not like the player chose to put that limitation there. IOW, the player likes everything else about the class, just not this one, specific thing and is asking the DM if, in this campaign, we can shelve this one specific thing for this one specific character.
And the DM's apparent answer is, "Nope. You chose this, you have to accept this, I will absolutely not take your preferences into account and you must anticipate that I will bring this into the game regardless of how you happen to feel about it."
/edit to add
There's other bits here as well. Playing a Dragonborn character or some other oddball race. Everyone agrees that there isn't a mechanical problem here. There's no powergaming going on. Nothing in the Dragonborn description talks about how Dragonborn are particularly feared or suffer negative reactions. That's something that the DM has added in. Now, it's not a case of the player accepting the consequences of his choices, but, rather the DM imposing consequences probably justified by some sort of nod to verisimiltude or setting fidelity or something like that.
Now, how is this not the DM specifically adding "consequences" that aren't even referenced in the rules? Same as having a motorcycle. Nothing in the game mandates that your motorcycle or your horse needs to be constantly protected. That's all on the DM. And the player is asking you to simply not do that because it's not interesting to the player.
See, this is what Backgrounding is meant to avoid. This sort of



for tat back and forth escalation between the player and the DM that the player, by invoking Backgrounding, is signaling that he or she is not interested in. Because, frankly, the player can never, ever win that contest. I put my spellbook in an adamantine, rubber lined, wax sealed box and the DM will just come up with another way to take away my spellbook.
I mean, good grief,
there's a reason that spells like Leomund's chest and whatnot exist in the game. It's the ultimate form of this approach to the game. It's a way that the player can get around the DM constantly picking the lowest hanging fruit to challenge the player.