Aren't there already tons of exhibits that engage with audience members to create new works? The only thing this idea is really adding is being rude to them.

Like, I imagine a good 60% or more of the people who are visiting an art museum have some experience painting, have maybe has a couple of classes. You'll have the occasional arrogant person make the claim and draw a stick figure, and those people may even be more likely to engage with such an exhibit, but I'd guess that roughly half the time someone steps up and makes a painting which is competent, though it may lack the artistic meaning audiences expect from greats. And of course time and materials are important constraints too.

I'm not a visual artist- I'm a musician. I can totally stroll up to a karaoke event or open mic night and handle myself. Most of my friends are visual artists, and they show those skills off when we play Drawful or Pictionary. Some of my friends ARE professional graphic designers, some of them do furry porn commissions, some of my friends run their own businesses where they mostly do other skills but are artistic enough to do a lot of the art themselves instead of paying someone else to.

So I imagine something like this would develop community. Maybe one person comes back once a month to do an ongoing series. Maybe someone makes a character that gets popular and others start to copy it. Maybe people try to re-create famous paintings. Maybe someone starts to make controversial things and the project gets shut down.