You know, your child has the right to counsel also - that's not affected by their minor status. If your child is arrested or some such, they have the right to counsel. Of course, we don't expect them to exercise that right for themselves, as minors - as a practical matter, they can't. We expect you to exercise that right on their behalf, as their guardian. But now you want to go way, way beyond that, and argue that because your child has a right to counsel, counsel must be provided regardless of circumstance, and regardless of your wishes as a parent and guardian - it is mandatory. "The concept still applies", after all.
You have created a standard for mandatory counsel that would, if applied to others who cannot exercise their rights, effectively terminate your guardianship of your own child, by giving some complete stranger veto power over your exercise of right and authority on your child's behalf. Well, okay - none for me, thanks, but if you're okay with that, it's your choice. Hope you draw a fairly laid back lawyer, and not one who decides that your brand of politics, your religious practice, your standard of behavior is somehow unhealthy for your child.
Which brings us back to the "right to counsel" which is distinct from the right to guardianship and is retained after being declared incapacitated. Can a father's counsel represent his child in a case involving incest by the father?