Not a good analogy IMHO. Players are not asking for hamburgers in a Korean restaurant. You're opening your table to a game of D&D 5e and players are expecting D&D 5e playable options that they can find in the D&D 5e player option books.
I disagree, I think it is an apt analogy, with the caveat that the player has foreknowledge of what they are getting into (that is, what restaurant are you going to...):
If you see a sign for a Sea Food restaurant, you shouldn't go in, look at the menu, and then ask for a hot dog (which is not on the menu).
D&D is "food" and you want to play ("eat"). Now, if you want to eat a hot dog (the PC race you want to play), but my restaurant (game) and menu (permitted races) doesn't include that, do you really expect me to run to the store, buy hot dogs, come back, cook them, and serve them to you? I really hope not, as that is pretty unreasonable.
Now, let's say you brought
a package of hot dogs with you! You just want me to cook up ONE. Well, that is certainly more reasonable and I would definitely consider it, but I have other things to consider as well: how busy is my restaurant, do I have the time to make a special order when other customers (other players) are ordering and eating what is already on the menu?
Suppose I make your hot dog and serve it. If other customers see you eating it and tell me, "Wow, that looks so good! Can I have one next time I come in?" then I might consider hot dogs would be good to put on the menu.
So, I see it as rather appropriate.
Also, several races are outside of the PHB. The only races as a DM I feel obligated to have are those. The rest are optional and I don't use most of them, but I've never denied a player who wants to play those in the PHB.
It would be more interesting to see how or why DMs or Players come to agreement than repeat replies to the effect of "I'm rubber you are glue."
The above analogy demonstrates what I've done in the past. I had a player in 1E/2E who wanted to play Draconians from Dragonlance. We went through the "dance" of "Sure, but you'll be from that world, others will be wary of you, etc.". They agreed, we had a good time, and another player (when his current PC died) asked if he could also play one? Basically, I said "Sure, how about you followed him here. Let me know if you are hunting him for some reason or friends/family and their to help him. Your choice."
When I started playing 5E, I incorporated Dragonborn and Tieflings into my world as cultures. I didn't have them before.