There's plenty of content in the Saturday morning shows other than just cartoons and competitions, people wouldn't have fond memories of them if they were literally just a way to link cartoons. I'm sure you could put some episodes on streaming with plenty of content once removing cartoons and other unclearable bits, the short lived Big Centre TV in Birmingham were repeating editions of Tiswas for a while for example, and I think The Family Channel used to repeat episodes of Motormouth before the TVS paperwork went AWOL.
I think Dick & Dom is one of those that would work well for that. The episodes on YouTube are about 1 hour 25 minutes once you remove the cartoons.
(Speaking of which, as it was the early 2000's they had landline, text and e-mail entries.)