And if all the PCs are Elves, no problem: there's no challenge for anyone involved.
But if there's five PCs and only one is an Elf, the very fact it's an Elf gives it an advantage the other PCs don't have: it can automatically succeed at something (gaining access to the King) where that same thing is a maybe-insurmountable challenge for the other PCs. Mechanically this reflects as DC 0 for the Elf and maybe DC 40 for the rest of 'em; i.e. guaranteed access for the Elf and guaranteed no-access for the others.
If the inn is truly open to all then sure, no problem. But the moment you hit "We don't serve their kind in here" you've got a species-based (in this case) penalty.
Here I disagree: if the higher Intelligence isn't reflected in the mechanics then it doesn't exist, no matter how much the Elves would like to think otherwise.
Yes it does, and that's my point. They auto-succeeded without even trying. No roll required.
We auto-succeed at a whole lot of things in real life every day. Ditto for the characters in the game world, only their world is underpinned by under-the-hood mechanics; and just because those mechanics aren't invoked all the time doesn't mean they don't exist.
Still means the Half-Elf has a mechanical penalty in this case, which is what the OP is trying to eschew.