Always_Ask_Questions,
“But, the impression from various halochos related to marriage creates an impression that if by the bas mitzva the girl is still in the father’s house, it is time to say tehilim”
This is an extrapolation that is well beyond the scope of those gemaros, which is surprising coming from someone with a strong STEM background. The fact that the gemara deals with a case does not mean that case is or was culturally normative. Given that halachos define the parameters of what is or is not permitted, they often deal with edge cases.