Look up autonomous home education, or unschooling - that'll give you a better sense of where some home educators come from. It's about facilitating, definitely not about setting tasks, questions, exercises. And no, you really really don't need pre-set learning outcomes when you are in a home education situation. I mean, you might say "learning to read" is a learning outcome, but that still doesn't mean the parent needs to have a curriculum or a plan to get there. Every child I know who has been autonomously home educated has got to reading when they were ready, and it simply hasn't been a challenge. The parents read to them, scribe for them, explain spellings when the child wants, provide materials of all sorts that have writing on them.
None of it looks ANYTHING like what we are used to in the formal education system, but I can assure you it really works.
I supervise lots of postgrads - MAs and research students too. What you say "Helping a research student know where to start, what is useful literature, how to frame a research question, how to organise diverse materials and providing constructive feedback on draft work is an extremely challenging job." is absolutely right, totally agree with you. None of it is discipline specific - we do co-supervisions across different subject areas in my faculty, because the important thing is having those skills in facilitating someone else to find out what they need to find out in order to learn, not knowing all the subject specific stuff to start with. Do you see what I mean? It doesn't matter whether I'm an expert in chemistry or not, if I know how to help my children find out what they want and need to know about chemistry, and I know other people who we can ask to help us.
For those of us who've spent our whole lives, as adults as well as children, in the formal education system, this is a real Alice through the looking glass challenge. Almost everything we think we know as professionals about how people learn best is just wrong when we apply it to an informal family-based context.