I had this situation arise. I asked my premed adviser and she told me to send one. Some schools listen to them and some don't. She said the worst thing they could say was "no." (though I can imagine worse things they could do).
I actually have written one to two different schools by email. I talked about how I was interviewing at a school in the area and that I was looking for a way to save money and time taken off work. I then flat-out said I was not demanding an interview or anything and that I would gladly return later for another interview because school x was one of my top choices (though it sounds like bs, both actually were).
As a result of one of my letters, I was offered an interview invite a couple days later. They never explicitly said my letter got me the interview, but based off timing (I had only been complete a few days and everyone else on SDN who had gotten interviews had been complete longer), I think the letter did it.
In the other case, the school wrote me back the next day saying they would bring it up at the next committee meeting and would let me know within two weeks about my request. I heard nothing.
So, it depends on the school. And I have absolutely no idea how it affected my chances at the schools (especially the one I heard nothing from). FWIW, I thought it was worth it to do, but that was only my own personal experience.
And if it is truly "prohibitively" expensive, I would definitely consider it. If you can't fly out more than once, then there would be no harm. If you can fly out more than once, I would weigh the decision a bit more. Definitely seek out the school specific threads (if you haven't already) to see if the school you want to send it to is receptive to the updates.
