Internal setting consistency.
That is not really setting consistency though. It is a meta restriction that has no place in a living world.
The PCs are first and foremost members of the setting's general population. A PC Elf, for example, is just like any other Elf in the setting. A PC Ranger is just like any other Ranger in the setting. PCs aren't special snowflakes just because they come with PC stickers on 'em, and I want the mechanics to reflect this.
I guess it depends on your starting point. We often start at level 0, but more recent editions the PCs start as already accomplished characters that are not standard people.
Regardless, it is not like you can plan a campaign from the beginning with every possible scenario in mind. I would rather have the flexibility to have an NPC with a new fun ability that I hadn't previous thought off and say - they are a snowflake, than have to make sure my PCs could do the same thing.
That said, the PCs might become special snowflakes because of what they do in the setting during their adventuring careers, but never because of their PC status alone.
Just like an NPC I would guess.
All my PCs might be martials now but it's ironclad guaranteed that won't always be the case, and I have to look beyond the immediate here-and-now at the campaign-wide picture.
But like I said, you can't possible predetermine every possible scenario and need that you will have 6 years down the road (the length of my current campaign).
Yes. In fact I'm sometimes that player myself, but only if someone else doesn't beat me to it.
If I'm playing an Elf and I see another Elf do something a typical Elf PC cannot, I ask (to myself) how and why can this be; and then in-character try to find the answers. And I'm by no means alone in this; if that NPC Elf has something that we can use, we want it.
I guess I have been lucky that my PCs trust me as much as they do then! But we have been playing for 30+ years together so it is understandable I guess.
Of course, it might not be the wisest idea for our characters to get it - e.g. let's say an Elf Fighter managed to Dominate a few of us during combat, on wondering how he did that we find a magic headband but the poor schlub PC who puts it on is in turn immediately Dominated by a major Demon who had been using the Elf Fighter as a puppet - but the opportunity should be there for us to find out if we can.
I guess my stance is: yes the opportunity is always there, but there is no need for me as DM to waste any time, energy, and thought on it when it is never going to be an issue.