The reason this show is still on the air is because of it's writing. It's not like Sesame Street or Barney that feel obligated to force basic learning on children. I remember when I watched this when I was young that many of the stories I could relate to that self-taught moral responsibility.
Also, there are a lot of in-jokes in Arthur making references to The Sopranos, Beavis & Butthead, Ultraman, and even Richard Scary. So, if anything, I find the show much more enjoyable as an adult.