I think poster made some really decent arguments about the lack of Compulsion knowledge.
I think another major issue going to be real world application of the idea. A BA can't drag their battery around anywhere where another female channeler might be without risking discovery.
The BA lives in the Shadows, also in the shadows. It takes great effort to ensure it is only the faintest of a rumour. Because it can do more that way. That also means 99.99% of the time you need to be and act like an Aes Sedai.
Given the massive disparity of channelers vs mundanes there's not a lot of benefit of raw power most of the time. Open conflict after all is close to the last resort of BA, the fact they reveal themselves so "early" is a mistake that eventually brings them down too.
Basically even if you could there is probably no reason to risk it until the rewards are great enough.