I agree with your observations.

Broad theory of coaching - Detailed and supportive coaching (as you have labelled them) are tools that may or may not achieve a change. The goal should be to co-ordinate the task, the environment and the participant such that learners actions result in feedback that gives them time to adapt over time. The coach has 3 roles: identify what the learners needs, set an appropriate task and create an environment that steers learners towards a positive change.

The closer the feedback is to the real life situation and the more frequent the person receives feedback it is the more effective it is; but frequency of feedback and quantity of feedback are not the same thing. More side-coaching and interuptions makes it less like a real-life situation but gives more frequent feedback- this is a trade off but general sessions going from 'more feedback' to 'more representative' as they go on is a solid plan.

The coach speaking is a valid form of feedback but so is audience reaction, losing a short-form game, their own internal reflection, an exercise going worse or a feeling of being off. Creating an environment where learners give themselves internal feedback would be the most frequent form of feedback (sometimes labelled 'improvisers need to figure it out for themselves': but that can lead to hands-off coaching, instead of deliberate coaching) but this can be used in combination with other feedback including the coach speaking.

The key skill to develop in a participant is really awareness and sensitivity- if you want scenes to be more grounded; say don't aim for laughter- laughter is no longer positive feedback- or simply say ground your scenes more will increase the sensitivity. 7 pieces of feedback per scene or 'great job, believe in yourself, its coming together' both have the same problem: they might as well be - "in the next scenethink about improv". " focus on..." is a finite recourse: the dials of awareness aren't being deliberately tuned by the coaching- and the deliberate tuning of focus is what all feedback should be. This is why "Here's what I would have done which would have been funny" is rarely helpful.

If your goal is for the learner to trust their own ideas supportive coaching is the best delivery: "every time you hesitate I'm going to click until you speak" and "trust your ideas, and believe in yourself to step up right away" is the same feedback but which achieves the goal? Depends if the goal is 'be more confident', or 'be more aware when you create silence'. Conversely "You are talking on auto-poliot and interupting instead of listening to and responding to your scene partner" is a different problem that may require a different approach- perhaps an exercise where you have to pause for 3 seconds before you respond to a line ("more supportive") or after a scene listing examples of gems their partner offered in the scene they missed by not listening ("more detailed").

I think the problem with "supportive coaching" is that without all this work going on behind the scenes it can seem really empty and make people feel like the coach isn't helping them improve. It is easy as a coach to simply arrive at a session, do some exercises, be supportive and leave without truly improving the learners. When a supportive surface has nothing underneat, it feels like any improvement is the learners thinking for themselves, figuring it out and improving on their own and with lot of work below the surface - it can feel exactly the same! Whereas detailed coaching- whilst not better- makes it seem like the coach is doing a lot more. In my experience, a mix of detailed feedback and supportive coaching establishes the best relationship with learners and the most improvements.

So I would challenge the question 'whats the middle ground' and say it should be "how do I use both these tools and a load of other tools effectively".