Reagan was the one who kicked off toy-based cartoons by deregulating the amount of advertisement time per show. Under the previous limits, shows like GI Joe or Transformers wouldn't have been allowed to be broadcast as they were considered advertisements. So, contrary to the idea that there would be more toy-based shows, I would argue that a Democratic President in the 1980s would completely kill toy-based cartoons from ever being created. A later President might support television deregulation similar to Reagan, but at that point you would have completely different toy-based cartoon shows.
I am guessing initially that toy-based cartoons would start out all right, but over a few years, a large fuss would be made about it and would raise it to court, maybe by 1985. It would not kill the shows per say, but it'd definitely cripple them, at least to where they would need to be changed. Some might change by making them into multi-media franchises like comic books. Given how Hasbro is connected to Disney, they'd probably be willing to make deals to make the shows better. Eisner was the one who led the charge to make better quality shows based on syndication right sales with the toys becoming an afterthought if everything was worth maintaining.
Granted, this is just Hasbro and I really only see My Little Pony surviving this and maybe Transformers if they decide to use the latter for video games or something.