It’s probably not fair to pin the demise of a beloved TV show on a nine-year-old boy; child actor Robbie Rist only joined the show for the final six episodes of Season 5, when the ratings were already dwindling.

Still, the addition of Cousin Oliver — Carol’s never-before-mentioned nephew who came to stay with the Brady's while his parents lived in South America (?!?) — was a transparent attempt to add a cute kid to the cast at a point when the rest of the Brady kids were nearly grown up, and he never quite fit in.

It’s not his fault the show was cancelled soon after, but Cousin Oliver’s name will still live on forever in TV infamy.

https://tvline.com/lists/worst-tv-characters-cast-additions-the-office-buffy-gilmore-girls/worst-tv-characters-late-additions-cousin-oliver-the-brady-bunch/

Oliver kept the scripts about the kids. The kids were older and the bubble gum scripts would not work. When Oliver joined, every episode beyond that point focused on Oliver and Cindy or Oliver and Bobby who were the youngest (except the zany Two Petes in a Pod). With older kids, the scripts would have to be more serious which was not the Brady Bunch. I understood why they did it but it just was too late and dumb.

This same kind of character happened with a lot of shows:
Patridge Family
Different Strokes
Family Ties
Happy Days