Bet isn't going to be able to reproduce Taylor's stuff anytime soon.
You say that, but if Taylor gave them access to it, and the information necessary to run it, then there's nothing stopping the humans to begin mass producing it in a week. (except permission from the other Fog maybe)
Heck, since Queen Administrator basically has YES amounts of processing power, Taylor should be able to run all of Earth Bet's farming, resource gathering, trading (not that they need that with the fully self-sufficient arcologies that she should be able to make) and crisis management all by herself. She may be an uploaded human mind, and not a true AI, but she is much less restricted than Dragon, and as long as she can run multiple instances of herself (and it seems she can, although slightly diminished from the original), and has access to self replicating material at this level, she should be able to take over the world (and even begin spreading through the solar system) within a few months or years at most. Self replication at this level, and such high processing capability should allow her to do pretty much anything she wants to.
The only problems here are the Endbringers, but as long as Eidolon doesn't make them break rythm and go all out, Taylor could out-create their destruction a million times over, even if she couldn't kill them. She doesn't know about Scion, and as depressed as he is, I don't know if he would even react. Maybe he would, and then she would have a problem, but again, she doesn't know to watch out for that.
The only thing holding her back is herself.