No, characters that are interesting in themselves without being intertwined in some grand epic conspiracy are fine. If they are, that's fine too. You can tell short individual stories about characters that just happened to be put in a situation and still be interesting. That characters have to have some major role in the grand plot of the series to be included sounds like some weird rule some delusional English professor came up with while being way out of touch with common taste.
It's not a rule an English professor came up with, it's just proper recognized story conventions. It has nothing to do with academia, then again intelligence isn't exactly something people should get mad at either. Hell, we're supposed to aspire to it.
In the case of Billy, he wasn't that interesting, and the problem with what you suggest is that Resident Evil has a huge, massive, bloated cast, mostly thanks to Capcom's compulsive need to create new characters that they just as quickly discard.
When you have a series and you keep adding more characters to it, you hurt the characters that already exist. Any time you make up a new guy or girl, it gives the characters you already made less time to actually...you know...do what characters are supposed to do.
So yes, when you write a story each character is supposed to have a role in that story. Sometimes they move the plot forward, sometimes they're there to set an emotional tone, or to make a main character realize something. When you create a new character to do something that an old character could have done, it makes the old character seem extraneous and that's just sloppy writing and makes the cast just that more bloated and convoluted. When you use a contrivance to get your "cool interesting" character that is totally unrelated to the events around him to get him into that story, that's even sloppier writing.
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