Before I moved up north, I used to live in Detroit, and the DIA was hang out of mine. It's an absolutely amazing art museum, one of the nation's little known best, actually. They have lots of security guards who are really careful about the crowds and who also seem highly trained to deal with folks who don't understand why touching the art is a terrible idea.
The museum administration has done something super clever to illustrate the problem. Just as you enter the museum, you'll see a bronze statue of a donkey that you're invited to touch or even pet. I don't know how long the donkey's been there. The bronze was cast in 1927, but the piece hasn't been in the museum all that time.
People will often do no more than just put a hand on the top of the donkey's head for a moment. Even so, a deep furrow has developed. You can see with your own eyes what hands have done to damage the piece.
A docent will usually stand there while school groups are going by, inviting kids to pet the donkey while showing them why it's very important not to touch any other piece of art in the museum.
And given the DIA hangs Rembrandts you could actually reach out and poke if you felt like it, that's probably an excellent idea! Even though, come to think of it, the few times I've seen the security guards get tough with visitors, those visitors were adults.