Well, I'm sorry, Piper. But, that is--unfortunately and undeniably--just what happened. At least, as far I'm concerned.
While I initially empathized with her plight, during the first month that followed Leo being put in cryostasis, her constant harping on it gradually began to have the opposite effect on me. So, I'm not surprised that it had a similar effect on Billie!
Or, more accurately, that Kristie was able to use Piper's obsession to gradually manipulate Billie away from the influence of the Charmed Ones.
My one ray of hope, despite the dismal writing behind both this episode and "Gone With The Witches?" That the reason the Triad is so obsessed with corrupting Billie is that--if allowed to remain under the Halliwells' tutelage--she might soon become powerful enough to succeed them, single-handedly! The Halliwells, I mean.
If that's precisely where the writers are headed with the series finale, I apologize for the unintended spoiler.