As long as we don't know what Sayu is running from, it's a bad idea to encourage her to return home. If she's running from an abusive household what does going back and "facing her problems" entail exactly? Tell her abusers/legal guardians off for their behaviour and go back to relying on them for love and shelter?
I understand that the current situation can't go on forever, but, to our knowledge, Sayu doesn't have any alternatives. Gotou doesn't offer her any alternatives either. Gotou cleverly doesn't tell Sayu to go back and face her problems, but waits for Sayu to suggest this option before encouraging her down that path in a manner vague enough to minimise her own influence on that decision.
Whilst I love the cunning in this move by Gotou, I dread to think the author may not be aware of how terrible this advice really is for Sayu. Everything is being presented as this profound moment of realization, when in fact it's a very twisted move by Gotou to remove someone she considers to be an obstacle. This can all be subverted or called out for the bad thing it is in a future chapter, but I don't trust the author and I are on the same page here.