In a significant amount of anime, the protagonist (and possibly others) experience one of the following parental situations:
Both parents are dead and are inconsequential to the story.
Both parents are dead, but one was more consequential to the story than the other. Based on my experience, it's usually the father.
Both parents are alive and are relatively normal.
Both parents are alive, but one is more consequential to the story than the other.
One parent is absent from the story, or dead. The other is still alive, and is usually more consequential to the story.
I'm going to name some examples, and assign them a letter according the scenarios I described above.
One Piece - 5. Luffy, Usopp, Shirahoshi, and Rebecca's mothers are all either dead, or absent from the story. Their fathers are all alive and very relevant. Ace's situation would fall under 2. His mother was largely normal, while his father is the pirate king and the catalyst for the whole story.
Fullmetal Alchemist - 5. Mother is dead, while father remains a somewhat prominent figure in the story.
Attack on Titan - 2. Both parents are dead, but the father had a much larger impact on the story.
Bleach - 5. Mother is dead, while father remains relevant to the story.
Berserk - 5. Mother is dead. His adoptive father is short-lived, but he still had an impact on Guts' life.
Cardcaptor Sakura - 5. Mother is dead, while father is alive and kinda relevant to the plot.
Fairy Tail - 5. Lucy's mother is dead, but her dad is alive for a good chunk of the story.
Medaka Box - 5. Father is alive and influential.
Shokugeki no Soma - 5. Mother is absent, but his dad is far more influential to the story thus far.
Ouran High School Host Club - 5. Mother is dead.
Sweetness and Lightning - 5. Mother is dead, dad is one of the MC's.
Garo: Divine Flame - 5. Mother is dead, father is quite relevant to the plot.
Katekyo Hitman Reborn! - 4. His mom is pretty normal, while his dad has actual ties to the mafia world, which is relevant to the plot.
The Prince of Tennis - 4. Ryoma's dad is a former pro, while his mom is an attorney. Being an attorney is still pretty badass, but his dad is far more consequential in the story, since it is about tennis after all.
Boruto: Naruto Next Generations - 4. Boruto's dad is a powerful ninja and the Hokage, while his mom is just a housewife.
Naruto - 2. While both parents were strong while alive, his dad, Minato, was the stronger, and had a larger impact on the story, being the Hokage and all.
Beelzebub - 3. His parents are background characters, usually for comic relief.
My Hero Academia - 5. For the most part, Deku's parents are support characters. However, his mother gives him parental support, while his father is working away from home.
The Disastrous Life of Saiki K. - 3. His parents are background characters, usually for comic relief.
Avatar: The Last Airbender - 5. I know it's not a Japanese anime, but I'm going to include it. Katara and Sokka's mother is dead, but their father is alive and well, and a prominent figure in the Water Tribes.
Kill la Kill is an interesting example. It doesn't fall under any of the scenarios I listed, since the mother is alive, more powerful than the father, and is super relevant to the plot. However, she's the final villain. I guess it'd be nice to have a character like her who isn't a villain, is what I'm saying.
That's definitely not all the examples, but it's just a few. Whenever an anime character has a missing/dead parent, chances are very high that it's the mother. If both parents are alive, it's usually the father who is more relevant to the story. If it's a shounen/seinen series, the father is usually stronger and/or more relevant than the mother.
My question: Why do anime mothers get the short end of the stick? In many stories, the mother is dead (Bleach). If they're not dead, then they're largely irrelevant (Katekyo Hitman Reborn). If it's a shounen series, they're often weaker than the father (Naruto and Boruto). If not, then they're the villain (Kill la Kill).
How come there's not as many series where the mother is the living parent, is relevant to the plot, is not a villain, and is the stronger parent in the case of shounen/seinen? The father tends to get all the spotlight. Personally, I would love to see more badass mothers in anime.
Disclaimer: These are all generalizations. I know that not every anime is like this, but I've observed it in enough series that I thought it was worth asking a question about. I also realize that my observations are biased mostly in shounen anime. I tried throwing in a couple of shoujo, but this largely remains a shounen trope.