Type: Setting, story cliché/wish-fulfillment
What made it popular: Various early Harems and Eroge
Cliche Level: High
Where can you find it: Most harems/ecchi are this, light novel adaptations like Oda Nobuna no Yabou are likewise the same
First of all we must clarify that by default Self Insert Stories always have a self insert protagonist, however not every self insert protagonist is in a self insert story. Basically in a self insert story nothing bad ever happens to the protagonist most of the time and if it does happen it is usually resolved within that same episode, and generally good things come to the protagonist like inheriting a fortune, a large group of girls falling in love with him for virtually no reason, succeeding in saving the world or gaining some power. Self insert stories pander to the demographic of your self insert character, the idea is to have their wishes come true with the anime. Like how harems have tons of beautiful, often supernatural and exotic girls falling in love with a total beta loser/virgin that wouldn’t be popular with the girls in a real life scenario. (Rosario to Vampire, To Love Ru, Sekirei Etc.) Or how Sword Art Online fulfilled the wish of many gamers being trapped in a virtual reality, where their only useful and practiced skills, in other words video game knowledge actually matter and can be the hero or someone important within that setting, despite not being actually more than some nerd loner irl.
Wish fulfillment stories can also sometimes result in quite niche stories that aim towards a very specific audience, like how Oda Nobuna no Yabou panders to the fans of sengoku era Japan. It has all the famous heroes and characters from that era, but the twist is that the protagonist is some virgin from the future and all these characters have been turned into girls who list for his penis. Yeah.
Why it’s bad: Incredibly predictable, no serious drama or development ever happens in these series, the story revolves around a single character and the rest of the cast do not matter and are only there to make the protagonist look cooler or be a part of his harem, one of the worst clichés since the entire story relies on whether you self insert into the character or not, if you do not the anime will come off as completely shallow/predictable/boring/bad and if you do self insert it will seem like a fulfilling watch, but you will still be empty inside since deep down you long for that world and know that you will spend the rest of your life irl. It is pandering of the worst kind.