Non-binary option for characters, please?

[Penthea]

Only if their system is stupid (not unthinkable given past experience!). They already do it for he/she, it's basically adding another item or two to the list of genders your chara can be, and another entry or two in the text that flag translates into.

For English at least, it's not that bad.

That's because "he" and "she" are both singular that this works so well. "They" is plural and depending on what is being said that can change the meaning of the phrase. The story refers to both groups of people and individuals together in phrasing very frequently, and replacing a singular word with a plural could very easily convey the story in a misleading manner. Simply replacing "he" and "she" with "they" can be done but it would definitely not result in an equally well told story.