I grow weary of Batman cartoons that my daughter can't watch. Must every DTV movie show a character being stabbed through the eye or having sex?
BTAS? The Batman? Batman Brave and the Bold? Beware the Batman?
Probably the most misplaced argument of the week.
Not at all.
Kelso's complaint was specifically about DTV (direct-to-video) movies. Everything you listed was a weekly television series, and thus beside the point. (And yes, the first two did have DTV feature installments, but the last one of those was a decade ago, so they're not relevant to a conversation about the
current DTV movie line.)
As I said above, the current DC Universe Animated Original Movies DTV line from Warner Bros. Animation is specifically designed to be PG-13 and more adult-oriented than anything WB Animation can get onto commercial television. However, as I also said, there are a very few DTV releases that are aimed younger.
Well, the blood is somewhat surprising in the PG-13 DC animated features from recent years (maybe starting with Gotham Knights).

It's more than you see in live-action superhero movies with the same rating, even intense stuff like the Dark Knight trilogy.
The problem is that the PG-13 rating is too broad. Because PG and R ratings are perceived by theaters (or DVD vendors, I guess) as less profitable, nearly every movie tries to edge its way into a PG-13 rating. Movies that would otherwise be PG slip in a bit more profanity or violence or sex to get nudged over the line into PG-13, and movies that would otherwise be R cut out just enough profanity or violence or sex to fall just below the upper limit of PG-13. So the standards of the rating have been stretched out in both directions, and it's become practically useless as a content indicator. (
Here's a cute video about the evolution of the PG-13 rating.)
But yeah, I have been startled by the overindulgent bloodshed in the past few DCU movies. It'd be R-rated if it were in live action. The latest ones have also gone for some fairly sophomoric and male-focused titillation, for instance the way Talia al Ghul spent the entirety of
Batman and Son in a jumpsuit unzipped to the navel. They really are trying overly hard to target a narrow audience of teenage boys, to the point of alienating other demographics. Which is something DC Comics has also frequently been guilty of in recent years.