Kids shows are often suppose to have a different lesson in each episode. Adult shows do have lessons sometimes, but not ones your children are necessarily ready for. The classics have lessons and things that adults also go through, and in a better environment for children. Although it's a good thing for kids to learn that they need to take care of their own mistakes, I think it's also good for them to know that adults make mistakes too.
Older television shows also had a better variety of setting and characters. Now everything is pretty much the same. Have you seen that show with that group of 20 something year old friends who all hang out at that one place in the city? Yeah, I'm not sure which one either! Once there's one extremely popular show, a bunch of others try to take off with very similar concepts.
Although modern television can be pretty funny, there will always be a certain amount of charm that only the classics have.