Who is ultimately responsibility?

What is a coach responsible for? Safety, yes. A constructive learning environment, yes. Progress, kind of?? I can be confident in outcomes on the basis of work completed (that's the purpose of an evidence-based teaching) but the learning curve contains different truths at either end. Near the beginning of the curve, the curriculum holds the key to learning. As we move further from the start, the curriculum holds much less of this power. Mature skills can't be programmed so much as discovered, and discovery is the responsibility of the athlete and not the coach.
The athlete-coach relationship remains vital but it needs to evolve where responsibility is concerned. Too many young athletes become stuck or develop learned helplessness because the coaching environment doesn't facilitate the transfer of ownership and responsibility.
From my point of view there are two separate dimensions to this phenomenon. The first involves young athletes having responsibility for extra-curricular activities such as injury-free. A small homework routine is vital because it signals to the child that they are responsible for more than simply turning up and doing what they're told to.
The second dimension of learned helplessness occurs when coaches fail to teach principles of movement. An explanation of how forces and motion create specific sporting skills provides scaffolding onto which the individual can layer what's unique about them. In the absence of this, children will simply mimic others. They plateau at the level of general competency.
The process of specification is the act of learning and adapting to the unique physical challenge that every body provides. Know your sport; know your body. 'Knowing' is the responsibility of the individual but it is incumbent on coaches to ensure athletes learn this lesson.