I think Saturday Morning cartoons on broadcast TV was on borrowed time by the early 2000s for several major reasons (in no particular order of importance):
1. The proliferation of cable networks catering to children, which aired programming during key daytime and early evening hours (if not 24/7)
2. Cable becoming more common in American households (so more kids have access to, and watch, those cable networks)
3. Media consolidation placing several of the broadcast networks under the same corporate umbrellas as the children cable networks they were supposedly competing with. (For example, Disney owning both ABC and Disney Channel)
4. Generally (at least IMO) the lack of a clear children's programming strategy by the broadcast networks. They were defacto obligated to provide children's programming thanks to the
Children's Television Act of 1990 (legally the obligation was on the local TV stations, but the networks took on the programming responsibilities on behalf of their affiliates), but had little clue on how to satisfy the Act's requirement for "educational and informational" programming.
5. The Act also made advertising to children more difficult, making children's programming less financially lucrative for the broadcast networks.
These problems combined to create an environment where children's programming just wasn't worth the hassle for the broadcast networks, resulting in the extinction of the classic Saturday morning blocks.
Given those conditions, you are going to need some MAJOR changes to significantly extend the lifespan of Saturday Morning TV. Butterflying away cable is nearly impossible, but you could butterfly away the Disney/ABC, Viacom/CBS, and Time-Warner/Turner mergers of the mid/late 1990s, allowing for more true competition in children's television. You could also tweak the Children's Television Act to allow for a greater variety of children's programming on television as opposed to the generic "educational and informative" programming specified in the Act, and make advertising to children easier so the networks make more money on children's programming.