I will throw out that at least Arknights has some of my favorite F/F ships across the cast in gacha, maybe my personal favorite. Though with the Doctor there are a lot of M/Doc shippers for certain, and it's interesting to me how that really doesn't reflect canon and especially compared to most gachas. The Doctor is generally sickly and frail, they're the last person I'd expect to fuck or have much/any libido. Plus there's a lot of stories The Doctor isn't even involved in, which I personally like. I prefer the Doctor to have more of a familial relationship with most of the characters they're intimately close with, and I view my Doctor as any of the following They/Them -> They/She -> She/Her. I also prefer to view player characters as their own character, and I'm not one for self insertion in general. In conclusion I avoid the male self insert side of the fandom as much as I can lol