As I've been in this position before, I feel like I can comment. First, my opinion- the only thing worse than asking a composer to work for free on a project is to ask many composers to work on the same project for free without a guarantee of anything.
That being said, I totally understand composing for films for free (at times). I'll be shooting my first short film soon and will probably be asking others for their talents for free (but in many cases, they are just returning the favor of me working for them earlier- building relationships does pay off).
Now, from my personal experience, I can tell you that the film makers that have asked a dozen composers to compose a scene or the whole film have not been quality films. Even the times I was chosen, there was little collaboration with the director/producer/editor and they were just choosing a completed package. What was even worse was a director that used different composers for different scenes; it made me cringe. That is just lazy. Collaboration with a director is extremely powerful and extremely important.
That being said, if you don't have a lot of experience composing for an original film, getting the the new, original clips and going through the experience of scoring it is priceless. I learn a ton every time I go through that process (paid or not).
I could have people submit scripts to me. Then I could choose one. Then I could have several film makers shoot it and then I could choose my favorite. I guess that might make a good producer, but not a good film maker.