Afro Samurai feels like the best example off the top of my head. Fist of the North Star and Ninja Scroll for sure. (In fact, Ninja Scroll might be your best bet.) I feel like the MK3 era has a helpless violence, mass death and paranormal terror in an urban environment element that evokes a similar vibe as Akira to me (plus all that blood). I feel like you can't just name any anime with punching in it and call it Mortal-Kombat like. There needs to be an earnest darkness, coupled with a twinge of morbid humor, extremely deep lore, a balance of sci-fi and fantasy, many characters, and lots of violence.
There's a surprisingly decent one I watched called Speed Grapher that, though it has no martial arts and far more direct references to sex than any Mortal Kombat story, the fighting-game-esque characters, dark humor and extreme violence seem kinda Mortal Kombat-ish to me.
