a protagonist you name yourself, can decide the gender of, and can choose personality through dialogue options
I would like to point out that if this is all it takes to be a self-insert protagonist, then you don't even need to look at open world games, you can go look at Fire Emblem Awakening and Fates which are
overly linear. You might have dialogue options (and in the japanese version of Awakening, your voice changes how all dialogue is said), but you aren't actually changing* any part of the story.
*Yes, Fates has a singular giant choice, but that isn't so much "deciding which faction to join" as it is "Which full price game did you buy?".
I'd recommend playing Dragon Quest 1-3 to see how a self-insert game with minimal player agency can be achieved relatively easily with RPG Maker.
DQ3 has the most bare-bones version of this and shows it fantastically. You decide name, appearance, and personality (in the versions that have that silly
mechanic), but the plot happens at the player and not so much because of the player.
- What are some good ways to write a "self insert" protagonist?
That's the key thing about them;
you're not the one writing them, the player is. We already have an entire
medium built around self-insert protagonists in tabletop roleplaying (such as D&D). If you want a game that has any amount of story in it AND the story is affected by self-insert protagonists, then it's much better to start from a similar perspective Game Masters do instead of the more common perspective of writing a story; You aren't there to dictate a story, you're there to make a world for them to make a story in. Others have brought up CRPGs and other more western series and they more or less aim to do this (whether or not they succeed is really a whole conversation of its own per series).
- What kinds of stories benefit or work with a "self insert" protagonist?
Probably the best ones are the ones where there isn't a story. Take an extreme example in Minecraft; there's no story, there's no guidance, there's nothing the game really says you should do. Anything you do is your choice. You are inserting yourself into a voxel sandbox and building what you want to build and doing it because you have a reason and want to build it.
But that's also a bit of a cop out answer. There's some random PS2 game I played way back in the day. The game was intentionally short with the longest path being 3 hours. It was entirely built upon choices you made. Sure, you always started in the same place, but there were so, so,
so many choices and the game was built in mind assuming that you'd play through at least a few times to really get a bite out of the overarching plot. Take that, but let it have different starting points, make each playthrough about what this specific character the player decided to make is going through for this historic event, and you have a fantastic (if short) game for this.
What are your opinions on "self-insert" protagonists?
I don't really have any issue with any particular one or even much of an opinion on them. Dragonborn is fine, Robin is fine, Erdrick is fine. But I'm not really sure what the point is when the goal is to tell the player a story. If you have this really cool story that you want to grip someone with through the medium of them actually playing it or you have a deep message to tell through the multitude of various themes that a video game can use or you want to unsettle people with how a certain mentality can lead to ruin, then a large part of that is having a protagonist you already know well and is serving that story. Having the player make the key protagonist that can undermine everything you are going for doesn't serve the story, game, or player.
But if you have a world? If you have this place you want to draw people into and feel like they are living there? Then you want, nay
need a self-insert protagonist. The player is adding a person to this world and thus shaping or even disrupting it by their very existence.
