If you’re doing an improv show and the only reason you take suggestions is to prove to the audience that you’re improvising, you must not have much faith in your improvising.
Everything I need is in my partner, on my partner, around my partner. The way she sits/stands inspires me emotionally. The way she gestures or walks across the stage makes me want to respond to her emotionally. Whatever she says has a tone I’m emotionally reading.
Emotions are at the core of all we do, not how well you can describe something/set up plot. When I gift you with an emotion I cast you. I also cast me. I am in constant response to your emotions.
A suggestion more often than not sets us up to tell the story rather than be the story. It also boxes us into a scenario we later might find doesn’t work or doesn’t surprise or doesn’t have tension.