The second you touch anything under a car, chunks of debris fall from every nook, usually directly into your eyes. As annoying as this material is when it's 40-years-old, it needs to be replaced when it falls off. You can spend hours scraping the underside of the car and clean all of it off then replace it with a more traditional paint, or you can simply do some touch-up.
When I welded on the frame of Project Street Fighter Mustang, I had to cover the welds and bare metal surfaces to keep them from rusting. Traditional paint would have worked with more preparation, but undercoating was really easy and was more consistent with the rest of the car.
I am planning on re-coating the entire thing as I go.