Do Warner Bros. and Disney still dominate the TV toon market like they did in the late 20th century?

No one is saying that box office numbers are the best indicator of popularity. Or that the immediate critical response a project gets will be the one that determines the quality of the project decades after that work has entered the public consciousness. They're just factors to consider.

This is a thread started by J Goldman, so you may consider your use of the phrase “No one.” to be rather reckless

Fair enough. But don't give JGoldman that much credit as he was pleading ignorance on how any property could be determined as popular (hence the really vague and naive question).

Really? I’ve always regarded him as an authority on most matters.

I have just eaten some hash fudge.

I'm assuming that JG has a skewed view on what's popular, seeing as he thought Waluigi is a very popular character but didn't realize that Frozen was a cultural phenomenon.

What sites do you go to to watch videos if you can't find what you're looking for on YouTube if I may ask?

If it is no longer on YouTube, then I don't care enough to search for it elsewhere online.
If it is a scene from show or movie, I'll look through Netflix, Amazon Prime, and the other streaming services if it is not on YouTube
Most videos I watch are by official channels and creators. I don't really search for anything specific on YouTube.

Okay.

To further answer the original question, Disney and Warner Bros (through Cartoon Network) are still leading the children's TV market. Even more so during the current health crisis, when schools are closed and children are stuck at home.
"Total day viewing of The Cartoon Network on Monday and Tuesday this week was up 58% versus last week, according to Nielsen data compiled for Digiday. Elsewhere, viewing of the Disney Channel was up 43%; Boomerang was up 31%; Nickelodeon experienced a 25% lift in viewers."
https://digiday.com/media/schools-shut-kids-linear-tv-ratings/

Streaming service usage is also high. Disney Plus reported having 55 million subscribers since its November launch. They originally predicted having 60-90 million by 2024, so they are way ahead of schedule.
https://www.cnbc.com/2020/05/05/disney-reports-33point5-million-disney-plus-subscribers-at-end-of-q2.html

Part of the reason for Disney Plus' higher than expected subscription numbers is the recent addition of Frozen 2 in March. It originally had a June release date on Disney Plus, but it was changed due to the health crisis.
https://www.theverge.com/2020/3/13/21179447/frozen-2-disney-plus-stream-date-coronavirus-avengers-endgame

Thank you sharing that. What about HBO Max?

It just launched on Wednesday, so there is no report of their subscription numbers yet.

Anyway, Disney Plus is more appealing to families than HBO NOW, which has more variety of content but not much new shows for children as of now.

Besides Disney and WB what other Hollywood studios run streaming services? I know Universal has one called Peacock.

Peacock is launching in July. As part of its service, it will have 8 confirmed animated shows, though only 3 will be ready at launch.

CBS All Access launched a few years ago with Star Trek Discovery being their major show. With the recent merger of Viacom and CBS, there are now plans to expand CBS All Access and include Viacom-owned Nickelodeon and Paramount films into the service.

As far as I can tell, Sony is the only one out of the major 5 studios that doesn't have a streaming service.

A lot of people know Adult Swim is Cartoon Network's adult animation block. Cartoon Network and Adult Swim are owned by WarnerMedia.

WarnerMedia owns Boomerang which only airs kids' cartoons and family entertainment.

How come Disney and Nickelodeon don't have adult animation blocks on any of their channels?

Are they afraid of hurting their family-friendly image?

Yes.

Disney tries to keep any mature content away from its channels and streaming service. Since it also owns Hulu, any shows aimed at adults are put there.
Similarly, Viacom (who own Nickelodeon) moves any adult animation to their MTV and Comedy Central channels

HBO had made a deal with PBS a year or two ago to produce and distribute first new episodes of Sesame Street. The OG of educational children's TV series. And they also have the child-friendly late-night satire,
The Not-Too-Late Show with Elmo. They have a bit more family-friendly shows and films (but my damn McAffee program just cleaned up my Chrome cookies and deleting my HBO Max password which I now have to reset AGAIN! and cannot presently look into what else they're offering).

I know about Sesame Street on HBO (there was that funny Elmo/Game of Thrones skit a few years back).

However, Disney Plus has much more films and shows that are aimed at families available at launch, with new MCU shows to be added later this year.

HBO MAX does have more variety for all age groups, but they have been using their HBO shows and WB films (and Friends) in their marketing.

Dreamworks is also crushing the world of animated television.
She-Ra and the Princesses of Power
Harvey Girls Forever
Kipo and the Age of Wonderbeasts

Yeah, I have been meaning to watch DreamWorks' Trollhunters series and the other Tales of Arcadia series.

So apparently, the most popular show on HBO MAX is the new Looney Tunes cartoons, with the second most popular is The Not-Too-Late Show With Elmo.
https://www.cinemablend.com/television/2547516/hbo-maxs-most-popular-show-revealed-and-its-not-game-of-thrones

Also, there is a New York Times article about the production of the new 200 shorts being produced. WB apparently hired a crew of lifelong dedicated fans to work on the show:
"[Series showrunner] Peter Browngardt quickly began assembling a crew of true believers, dogged fans who had watched the originals on syndicated TV.

He enlisted the animator Jim Soper for character design (“I’ve been waiting my whole life for this call,” he told Browngardt) as well as the storyboard artist Ryan Khatam.

A lifelong fan, Khatam had collected and cataloged QuickTime versions of every “Looney Tunes” short since their beginnings in 1930 — something the studio itself had neglected to do."

https://www.nytimes.com/2020/05/29/arts/television/looney-tunes-hbo-max.html