And I'm honestly pretty skeptical that even when judging "blind" the judges don't know who the person playing is.

As a former professional musician (I'm changing career path now), no, they don't usually know who the person playing is. Usually, there are LOADS of people doing auditions and the competiton is fierce and if it's orchestral auditions, we're all playing exactly the same excerpts (according to our instrument). When it reaches a professional and high level, it can make it really hard to guess who is playing what. We, for sure, don't play all the same, and yes, we all do have some uniqueness that makes us "characteristic". Heck, even the fact that we have different instruments from different luthiers makes our sound different from each other. But in professional auditions, ESPECIALLY for orchestral auditions, you REALLY need to respect what the score tells you to do, meaning there's not that many space for interpretation. There are SOME cases in which it IS unfair and the judges know BEFOREHAND that X or Y person will compete and are expecting to hear that person. But they know it beforehand or look at the candidate information. Basically, it can be possible to guess, but it's not that easy at all as you seem to imply.

NOTE: This is based on my personal experience and country.