It's possible there is some selective memory going on here. The term "fat cat" has been in common use for quite a long time. That tells me that fat, lazy cats have been a cliche for a long time. Maybe you just didn't see them.

At any rate, I saw something recently that I thought was pretty cool. This guy made an exercise machine for his cats. When the cats use the machine, they earn a reward in the form of food. It looks fairly easy to build.

http://youtube.com/watch?v=f5Fg6KFcOsU