It depends on the needs of the campaign.
If I'm doing something that is the RPG equivalent of a game of pickup basketball, I generally don't care what options the players are using, so anything goes, as long as its genre-appropriate.
OTOH, if I'm running something that has a strong story/mechanical core around which I built the game world, I can be quite restrictive indeed.
This.
If all the characters are members of a thieves guild, then a plate-wearing paladin isn't going to work. If the campaign is "Everyone's a kobold", then well, everyone's a kobold. If the campaign is "Explorers to the Jungle Continent", I want everyone to start from the Old World (where certain races/classes are from), and New World options (races/classes) open up as they play.
If the campaign doesn't call for limits, then I don't place them. There are certain classes I think are weak or dumb, but the only thing I stop are broken/OP options. And usually my objection is not
what someone is playing, but
how something is played (Hello, Dragonlance races). But I find it hard to swallow pixies from a tone perspective.
Another important note on limits: If a player really wants something that violates one of those limits, I'm fine with working in a way to defy it if it's interesting, and if nothing else we can reskin something. For instance, let's say a Warforged in Athas. Athas is a world where there's little to no metal. Ok, Warforged are creations of bone and stone, crafted by the Sorcerer Kings to be unwaivering guardians and bounty hunters that can travel the blasted earth without fear of exhaustion. A Deva with one of the New World classes and
sparse memories of the Jungle Continent would work fine.
One of my favorite things to do with limits is, once the players have made their characters, say "The races you've chosen are the only common PC races in this setting." After that point, any other race would need some sort of unique story (First of its kind, Last of its kind, ONLY ONE of its kind, new race on the planet, etc).
What I like about Kitchen Sinks is
working that thing into the setting. Eberron is a great example of this - the design goal of it was "If it exists in D&D, it exists in Eberron", so they intentionally made choices to work various things into the setting. You could ignore them, because they were often linked to geography, but if you looked (or you thought about it), you could work anything in there. So once you pick something oddball, make it
work within the setting.
As a player, I love wacky inhuman races and exotic classes, so I'm all for non-strict limits. Any sort of "You can't play this" always makes me
want to play it.