It's not a crazy idea. It's done all the time. You could also buy a Lee's specimen cup, the kind of cup the LFS put your fish in after it's caught, carefully drill holes in it, hang it in the tank as close to the lights as possible or buy a guppy breeder net, etc., etc.
Although I don't understand how Chaeto could be all over the place. It grows in long tough spaghetti strings. Tell us more about your experience with it breaking up. Where is the ball of it usually placed in the tank?
Along with Chaetomorpha, I like to have several varieties of Caulerpa growing in my tanks. When it starts to get too much, almost out of control, I add an herbivorous fish. I've had many types of Tangs, Rabbitfish, Angels, and Blennies to eat algae in both large and small tanks. I love algae. It's such a great filtration medium, makes places for more bugs to grow to keep nusiance algae in check and looks cool too.

Edited by Mark Peterson - November 28 2008 at 11:11pm