Worst Study Ever?

This study has so much wrong with it that it's not even funny. Start with the horrendous title for the article (to be fair, not the fault of the study writers). But move on to the core "problem". The study asks the question, "Are irredeemable villains and inept cops appropriate depictions for cartoons."

Now let's leave aside your particular issue that you may have with this issue (perhaps you think that cops ARE incompetent or criminals ARE irredeemable) and just look at their core assumption. "Cartoon depictions predominantly feature these two archetypes."

I don't grant that premise.

Batman deals primarily with two police personalities, neither of whom could be described as inept. One of them doesn't like Batman and considers him a barely acceptable vigilante, but that's not "incompetence" and, if anything, represents two valid world views that police might have about a Batman running around.

Now let's look at whether or not the criminals are irredeemable.

Certainly Joker, Penguin, etc are, in fact, irredeemable. They're the psychotic mass murderers. Even the most liberal sociologist would surely concede that a serial killer with multiple souls black marking their heart are "probably not redeemable".

But the "next tier" of villains is anything but. In fact, I'd argue that many of the spider-man villains are depicted as almost too sympathetic. The guy who is "forced to rob a bank to feed his family" is a pretty cliche super villain motif. As is the beleagured inventor who has his inventions stolen by the giant corporate behemoth and sets his sights on hurting said corporation. These villains frequently reform.

Catwoman works with Batman (and they have clear romantic attraction)
The Mad Hatter realizes what he's doing was wrong
Eddie Brock has the venom suit removed from him and goes back to normal
Harry Osborne gets control of the Green Goblin
Black Cat has a romantic entanglement with Spider-man and goes straight
Rex Mason is a crooked CEO who becomes the hero Metamorpho

Those are what I could get from memory but I'm certain there are others. Worth mentioning is that the comics are full of this treatment. Nearly the entire roster of the West Coast Avengers (Wonder Man, Vision, Scarlet Witch, Hawkeye) started out their comic careers as villains. Emma Frost has become a good guy. Sinestro is currently back to being a green lantern (although not exactly a "good guy") and the newest green lantern is a former car thief. Braniac's descendent Braniac 5 is the leader of the Legion of Super Heroes.

Finally, I'd be remiss if I didn't point out that these shows do not represent the most recent comic book television fair. Left off this list is 2 different X-Men series, Iron Man cartoon, another spider-man cartoon, Batman Brave and the Bold, Young Justice and others. I'm always skeptical when I see three shows cherry picked across two decades. Now it's possible they went with some criteria (most recent three shows with 4+ seasons) but that's not clear from the article.