Here is a New York Post article reviewing some of the many annoying child and teenage actors on hit TV shows right now. I haven't seen any of them, so I'm not sure how central they are, but it sounds like they're at least regular cast members, some of them at the core.
If there are so many of them littered throughout popular shows, the general audience appreciates it, notwithstanding a vocal minority. And even if the general audience doesn't care for a particular character, that's more of a failed attempt at the goal of creating the "prominent child character" that the audience craves. In today's climate of nuclear family-centric cocooning, viewers just can't get enough of watching children.
However, this isn't the only time when you would have been assaulted by annoying kids when turning on the TV. During the previous heyday of permissive parenting in the Mid-century, one of the most popular shows was Dennis the Menace, starring a more sympathetic but still off-putting Baby Boomer brat who couldn't act. The less popular yet more iconic show Leave It To Beaver starred an even more annoying kid who couldn't act.
Circa 1960, status-striving and dog-eat-dog competitiveness was nearing a low point, so at least those earlier examples would not have made you angry with their smug dismissive attitude. Still, they were children who couldn't act, they were central characters, and they were going to get on your nerves for being so dorky, bratty, and wussy.
As Mid-century cocooning had all but melted away by the 1980s, it was damn unlikely that you were going to suffer annoying children on television. Here is a site that lists the top 30 shows in the Nielsen ratings for each year, which you can browse if you're unfamiliar with them.
For the early and middle parts of the decade, there was nary a child to be seen, let alone a central character whose immaturity and inability to act would have made you change the channel. There was that blonde daughter from Family Ties who was a mopey sourpuss, but she was mostly out of the picture before she got to high school. I'm sure there are other marginal examples like that, but none where they're one of the main characters.
What's striking about the hit shows back then is how grown-up everyone is. Dallas, Magnum P.I., Cheers, Miami Vice. Viewers then were so maturity-minded that they put The Golden Girls, a show about four senior citizens, into the upper layer of ratings. Directly related to that is how unrelated most of the characters are — annoying kids tend to crop up in shows that focus on families.
Toward the end of the '80s, as cocooning is about to set in, there were still only a couple of annoying kids on TV — the son Jonathan in Who's the Boss? and Rudie from The Cosby Show.
Then as the family-centered shows of the '90s rode the wave of helicopter parenting and cocooning, we got a deluge of annoying kids. Darlene and DJ from Roseanne, the little boy from Family Matters, the Olsen twins and Stephanie from Full House, the blond nerdlinger from Step by Step, and all of the kids from Home Improvement.
Everybody's favorite show about nothing, Seinfeld, was a holdout in this regard, and in hindsight was a key factor in making the show so enjoyable — no fucking kids. Not even teenagers. It was more of an ironic and self-aware incarnation of Cheers adapted for the postmodern Nineties.
These changes back and forth are the result of folks being more community-minded and public-oriented vs. more family-minded and home-oriented. The community and public places are not made up of children, but adults (mostly). Only when people start locking themselves indoors do they dwell on the ankle-biters that are part of private, family life.