Having a set form . . . does it hurt improv?

For the new year, I’d like to broach any interesting theory for those that think improv is best when it’s free form.
During my time at Honolulu Theatre for Youth, I performed in a show directed by David Furumoto called, “Wondrous Tales of Old Japan.” As a side note, it was one of the best experiences I had at HTY. But one moment that stood out in my memory occured during one of our note sessions. It was the moment that David likened the style of Kabuki acting to a crystal. When you shine a light through a crystal it creates a rainbow of colors that shine in all directions. The crystal is the style and the light is what the actor brings to it.
I see this in Improv shows that have a set form. Sometimes set forms can create stagnation because people see it as being too constricting but if you work on the skills that set good improvisers apart from another (e.g. relationships, agreement, establishing who, what, where) you can create a rainbow of colors that may not be possible when you are without a form because you don’t have any time in performance or rehearsal to do so.