Ian at Createquity has a really great, nuanced look at submission fees for a composing competition. You can find it here.
I know that submission fees for playwriting competitions are the subject of some controversy in the field. The Dramatists Guild, if memory serves, takes a blanket "no" stance towards them. I feel pretty torn. There are lots of organizations out there that are basically scams: they take money for submissions of, say, ten minute plays, and then that submission money goes to pay the winner's purse and, of course, the people from the organization. But winning the competition won't do anything for the writer and the purse is generally small... $200, say.
But then there are organizations that really are playwright service organizations like Bay Area Playwrights or The O'Neill. They have submission fees, and its hard to fault them for it. They have very few sources of revenue beyond donations, being involved with them really can help a playwright's career and they genuinely exist to help writers. Having a fee (and really, $35.00 isn't a lot of money, although if you're applying to a bunch of programs it adds up) helps control the flow of scripts as well and makes sure that applicants are serious about applying.
So I'm saying I see both sides of it. I have a feeling I'm going to get some grumpy comments about making money off the backs of writers, who are already underpaid and exploited. And I'm sympathetic to that as well. Perhaps something like in admissions to schools where there's a fee (often a lot steeper), but you can apply for a fee waver would help.