Managing the schedule in coaching support

In coaching support, we often see ourselves as a resource.
We are "at the disposal of" clients, there to help them as best we can: sharing experience, making introductions, or offering time for reflection and decision-making support.
In this posture, it may seem logical that managing the schedule is not one of our concerns. It is the clients who need us; it is up to them to reach out and arrange an appointment when they feel the need.
And then we might tell ourselves: "But if I set no limits, I'll be overwhelmed: they'll call me day and night!"
👉 Well… no. It's actually rather the opposite: very few requests.
I've always found that surprising.
Experience shows that if we don't take charge of the schedule: either with a pre-set calendar (efficient but often too rigid), or by fixing a date at the end of each session (my preferred approach; you just mustn't forget!): then appointments between coaching sessions are often terribly spaced out and we miss a large part of the work.
We don't bring to the person what we could have. That's a shame.
And it's not a question of price; I'm also talking about programmes that are either free or where support isn't counted in number of appointments.
Why do clients miss out on these contributions?
I admit I've never really understood….
My hypotheses:
They don't dare bother us too much (I've always explained how it works clearly, though)
They're so overwhelmed by "everything" that they no longer see time passing.
Or… they're avoiding us: I bring them no value and they'd rather skip appointments
I think above all that we underestimate the value created by these exchange times. They don't seem like priorities. Many underestimate what doesn't look like "production."
With our heads too far down in the work, we waste time by deliberately not taking any.
So as coaches, it's our role to explain this… and not to let go of calendar management!