It's called a "missed opportunity" fee. Some of the coaches here do charge it, because by going to a competition they are missing out on other income opportunities they would have had otherwise. My coach doesn't, so I don't know exactly how the others calculate it.
I do understand why, in theory, as when these coaches take 10 skaters out of state, they are giving up the rest of their lessons for the 3-5 days they're gone. If they're only charging expenses and a lesson fee per event, then they would lose considerable income. And, for these coaches, that is their livelihood, they don't have other jobs.
My coach charges 1/2 hour lesson fee per event (so if I do dramatic and fs, it's a one hour fee). Considering she spends at least an hour per event with warm up and everything else, then waits for results, it's more than fair. For out of town comps, all of her skaters split hotel, gas, etc., but she doesn't charge for food or other costs she would incur anyway.
And Loops, yes, you can go without a coach. That just means that you have no one that is allowed to put you on the ice (hold your water bottle, jackets, etc.). Friends, unless they have the proper certification, are not allowed down by the ice. Lots of adults do this regularly as it gets expensive to take your coach to out of town competitions, especially if you're the only skater.