Reason 2: She'd be overshadowed on team red at Survivor Series
Should Paige have joined RAW's team at Survivor Series, what then? She'd likely have just been in the match and gotten eliminated.
With the spotlight likely going to Asuka and Nia Jax, there wouldn't be a lot for Paige to do on RAW's side. She'd feel more like a third wheel than a huge part of the team.
Conversely, if she were to go to SmackDown and finds herself on their team in lieu of Charlotte, she'd have a bigger spotlight on her. She'd instantly be one of its strongest players that would make the contest less unequal and could well be the star of team blue. In turn, it would boost her standing more going forward.