I'm genuinely confused as to why she remains such a popular character. Does she really have the same appeal as Deadpool? Or am I underestimating the appeal of "attractive lady does rude and violent stuff"?
Well there is a not-insignificant subset of the fanbase, especially women, who often like characters like Harley, simply because "she's a *****." I've actually heard this, when I've asked women over the years why they liked a particularly rude/violent/abrasive female character. The answer I often get is "she's a *****." Nothing further, that's it. I think it's because that personality type, is the one most often used, and allowed, at least when referring to female characters, to speak their minds, and say things that will often piss off guys. An outlet for female frustration, if you will. People expect Harley, and others like her, to call out the asshole guy in public for being an asshole, and they don't get shut down by society as being rude or whatever. For a group thats been conditioned for generations, to be polite, be nice, don't speak out as that's unladylike, etc, even if it's a justified speaking out, these characters are of then the exception to that rule, so they become a huge draw, and have a huge appeal.
And for that part itself, I really don't have much of an issue with Harley, or others like her. I do think it's possible to speak your mind and NOT be a *****, but we're talking mass market entertainment, they're going to try and use the most efficient, minimalist concepts to appeal to the widest audience. So "***** girl" is a quick and easy trope. The few examples of a woman who speaks her mind, and doesn't back down to confrontation, who aren't also portrayed as a ***** trope, are about as rare as bigfoot.
I just personally dislike, with Harley specifically, the glorification of her insanity, as a positive aspect of her character. Well, that and her being an actual villain, who fucking kills people because she likes it, and helped a violent psychopath for years to kill and torture thousands. She doesn't seem contrite about her past crimes, and they never frame it like she is. They just frame it as her deciding she's not gonna let an abusive man order her around anymore! Which, yeah ok, cool? You still happily killed a lot of people at his side, and don't seem to regret it at all. You just still gleefully run around doing crimes (which they establish in the opening of the new SS movie), and consider these jobs like some kind of vacation or something.