Just to center back on the title and first post of this thread for a moment:
What anime could someone find compelling if they so far haven't liked much anime?
I'm old enough to remember when liking anime was a pretty weird thing in the US. There was no manga available, much less having its own section in Barnes & Noble. If you wanted to watch an anime movie (pre-streaming!), there wasn't even a section for it at a rental store. Anime would be mixed in with Kids films like
Aladdin and
G.I. Joe: The Movie. It was uniformly associated with Japan, and mostly called "Japanimation", and people thought it was super weird. And honestly, a lot of it was. And people thought anime fans were super weird. And honestly, a lot of them were. If you walked down a high school hallway (no one older or younger knew about anime) you could easily find the freaks/losers who might go on about some
Ranma 1/2 bootleg they got:
Anime fans looked pretty damn close to this, and it didn't do much to make the general public want to join them in learning about anime. Before it became cool to call yourself a nerd, back when San Diego Comic Con never had A-list actors walk through the doorway, anime was a doorway into creativity and wackiness that mainstream culture rejected. It was 10x more creative than the normal films out there, and owning being an anime-lover was like turning your Outcast status into a badge of courage. You were a free-thinker, a creative, an individual.
Of course, in and of its nature, that means a lot of anime is not easy to get into. And as it has gained a wider following in the US, the amount of anime available has ballooned...but not at the end of the spectrum where it's become more accessible.
Reel Rundown has put together a lovely
primer on the genres of Anime, and the sub-genres of Anime. And the sub-genres are where shit gets really weird. I'm sure people have done whole Anthropology dissertations on how an anime gets popular, then the central idea from that anime is piggybacked by other anime, then the conventions of those other anime become part of what's seen as the original idea. All this is tied up in the specifics of Japanese culture too, so that's how we end up with a common sub-genre like "
Harem".
Playing on the pretty normal Japanese trait of a guy who'd prefer to run away from a romantic encounter rather than deal with the stress of one, this sub-genre inevitably features a nice guy main character who ends up with a bevy of beautiful babes of all sorts virtually (or explicitly) throwing themselves at him. There are so many cultural aspects and anime tropes being built upon in even the most basic of these stories that I wouldn't recommend it for anyone new to anime. It would probably just come off as creepy, juvenile, and even misogynistic. (And some of them may well be!)
In fact,
most of the sub-genres of anime are built on decades of series and films and manga being made, a kind of cultural piling-on, building the national conversation about what makes a gratifying adventure of this type. Whether it's
Shounen anime or
Josei anime, these films are aiming at a very specific thing and I think odds are not great that a Western viewer will really appreciate them if they haven't been into much anime before.
Even from the main categories of anime, it's important to keep in mind that almost all anime is made for the domestic market, without much thought to how it will play outside Japan. If it's not successful on NHK (or wherever it airs) then they'll probably never have the chance to export it to foreign markets anyway. My guess is that this is why a lot of anime seems to have a higher proportion of over-the-top comedy/romance/tropes in the first few episodes and then straightens out. They need to capture that viewing audience early. But these anime are still made
by Japanese
for Japanese, and lemme tell you brother, it's a whole different emotional world there. I lived in Japan for over five years, and the cultural subtexts are killer. In good anime, a lot of that gets worked in to the drama or the romance, and I'll admit that made it harder for me to understand before I'd experienced it. Even after knowing
why, for example, a romance series will go 22 episodes and have declarations of undying love but
never even have the main characters kiss...it still doesn't mean I respond to it. That means even a relatively straightforward Drama like
Kanon is not something I'd recommend to someone not already an anime fan. The characterizations and motivations are likely to be hard to grasp and not resonate.
All this is to say that perhaps the best way to find a gateway into anime, is to look for anime that seems somewhat similar to Western films already being made... just with a unique Japanese twist. What I think Japan does really well is to come up with nuanced visions of the near-future, and to compellingly direct action. As Western films have started adapting many of the aesthetics from Japan (starting with films like
Blade Runner) and Western cartoons have started animating action more like Japanese anime (starting perhaps with
The Powerpuff Girls and
Avatar), Western audiences have perhaps gotten more accepting of anime and willing to check it out. But they still need something familiar to hold on to at the start, like the police procedural of
Psycho-Pass. Slight sci-fi elements are a lot easier to take in than something like an anime that mostly exists in a virtual world (
Sword Art Online) or is entirely in space (
Martian Successor Nadesico). Shows like
Psycho-Pass hearken back to the anime that helped break into the Western world in the first place, films like
Akira, Ghost in the Shell, Appleseed, and even
Macross Plus.
I'd recommend starting with this Action/Sci-Fi genre, as it's just Japanese enough to justify watching these instead of live-action Western films, and yet the animation style, voice work, and story development tend to be fairly realistic, For people who are turned off by CGI too, this has the added benefit of being able to depict insane action sequences in ways that aren't possible in live action films without lots of CGI. Collider has a good
anime good for beginners here too, and they list several action and sci-fi anime. For me, just the fact that Western anime fans have gone from being outcast weirdos like in the top picture to a mix of fun quirky people like in the picture below.... well, it warms my heart and makes me feel like maybe there's a little anime fan in all of us.