Its important to remember that in the full scope of things, 'Anime' as a genre doesnt actually exist. 'Anime' is just the Japanese word for animation. Its honestly silly to have an entire subset of animation labeled differently just because it was drawn in one specific country. USA? Cartoon. Canada? Cartoon. France? Cartoon. Australia? Cartoon. Japan? Nope, we call that anime for some reason. Its just silly.
And yeah, its easy to say cartoons are more targeted at children when you specifically exempt 'adult animated series' as a subset of cartoons. Where do you draw the line between those two? You cant ask for animation of a higher quality and scope and then exempt that shows that specifically do that.
I guess my point is, dont get caught up on trying to label animation as a million different things. Just enjoy whatever you want and dont let 'subsets' skew your perspective on what you could be enjoying. As for me personally, I never caught on to Japanese animation because the plots always seemed too ridiculous and they use a lot of animation shortcuts, but that didnt stop me from enjoying My Hero Academia or Jojo's Bizarre Adventure