Many factors have probably caused Saturday Morning to fall into obscurity. But I do feel cable has contributed to it as with most things deconstructed by our entertainment. First off, the reason Saturday Mornings were so strong in the past, as you indicated, was the fact you couldn't watch cartoons 24/7 as you can now.
Sure you had syndicated cartoons like Tom & Jerry, Underdog and other classic toons, but for the most part Saturday Mornings still were strong because the good Toons were on and if you wanted to watch them, you had to get up and do it. Regrettably there were no such things (except in television studios) as VCRs, so you couldn't record your shows.
Also because Saturday Mornings were targeted at kids and young teens, shows were mostly aimed at them, but some were also well-written. Not all things were animated, I can recall live-action shows like 'Big John, Little John,' 'The Far-Out Space Nuts,' and 'The ABC Weekend Special.'
Unfortunately what killed Saturday Mornings was technology I fear, with the advent of VHS, cable channels and now DVDs, why bother getting up watching animated shows, when you can either catch them again at a later hour, or simply purchase the collection at Wal-Mart or Best Buy?
Or catch a forgotten episode on YouTube? Though CBS and CW is barely keeping Saturday Mornings alive, most of their programming has now been aimed by younger children, since most now are the only ones who still sit in front of the tube on Saturdays and watch television. That is, if they're not out shopping or playing video games.
So in all reality, Saturday Mornings as we fondly remember have gone the way of the Dodo, which is sad, because sometimes I do yearn for the days when you got up and watched the animated and kid programming the networks had to offer. Even if most of them weren't all gems. 8)