So, supposedly one way into concert dates is doing well in piano competitions. However, piano competitions are expensive. Looks like $200-$300 seems about a normal entry fee. And then there's the travel, missed wages etc.

I did a bunch of competitions pre-conservatory, but either it's much cheaper in that age bracket (under 18), or it was much cheaper at that time (late 90s), or my piano teacher was secretly paying a lot of my fees. (Which was possible. I was her one work-study student, and she's that kind of person.) The purpose of those competitions was different, too, as I recall--more about getting exposure and critical feedback from professionals, not about getting an agent. I don't even think there were agents at those things.

Are piano competitions worth it?

(Are they just scams? They must rake in a lot of money at $200-$300 a contestant...)

There are a lot of competitions these days. Makes you wonder if the world needs so many!
Sorry, I can't really comment much on the kind of competitions you are talking about, because I have only ever been in one competition and that was 1 1/2 years ago - an adult amateur competition. I went in not to win (I knew there was no chance) but just as a personal challenge to myself and also to hang around with other piano geeks like me for a few days. I believe I paid $175 to enter and feel that I got my money's worth. I did make new friends and I proved to myself that I could do it and not pass out from being too nervous (it was close, though.... ).

On the other hand, the jurors don't sit on the jury out of the goodness of their hearts, and I think they probably expect quite nice accommodation as well.

Yes, and they do have a huge job - all day listening/judging/critiquing piano playing for several days in a row. They too are missing wages but then they are compensated for being on the jury. I wonder how much they are paid?