You do realize that Becky's game appeared years after the original, right? At that point Resident Evil was supposed to be a one shot. Of course she had a fucked up continuity. And apparently, she had no ammo in RE when confronted by the hunter (if my memory ain't messed up).
Using another police officer in 0 would make things weird. Maybe Kenneth would work, but then knowing that you played a future-to-be-killed character would be a major detractor.
Remember that she survived RE0 and RE1. It made sense to show her broken down and seeking refuge in the only mansion in the vicinity. She wouldn't know the mansion was overrun by zombie clones. Billy couldn't go because he had to get the hell out of there and bang someone's mother.
Yes, I liked the game. After that one, the series has turned to trash. Even RE4 is a bit caca.
I'm not talking about the situations themselves. I'm talking about how this could be fixed. It's OK that she went to that mansion. Well, she had to because of RE1. But her reaction could be different. I dunno, maybe a radio talk with someone from her team, or something like that. But "I'm gonna go there all alone" looks kinda stupid.
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About confrontation with hunter: maybe so. But then it's even more stupid that they always tried to split up as soon as possible in RE1. I understand that this is necessary for the genre, but there are plenty of details that could be changed in order to make more sense.
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BTW, RE4 is not a horror, but it's a damn good game with thick atmosphere of hopelessness, interesting item management, solid gameplay and awesome cutscenes with good actor play.
Even RE5 is OK as a coop game. Boring if you have to play it alone. RE6 is garbage. Both coop and single player. I hope RE7 will make me crap my pants (but hell, I'm not gonna play this in VR - don't wanna die)