I suspect that the parents are right. No teacher is perfect and sometimes we need to take on board external ideas- rather than express indignance that a parent dares to care about how their child is being taught.
I thought you gave a good explanation.
Now, here's another of my radical ideas.
Perhaps the teacher is a good one faithfully adhering to traditional piano teaching principles.
But on this particular point, piano teaching is fundamentally flawed.
I say this because in my very inexpert opinion, almost no beginners succeed in ever breaking the hesitation habit and playing fluently.
Sure, the kids who advance through the grades, go to conservatory, become classical pianists or piano teachers do.
The other 98% or so eventually drop. They may have gained a lot of benefits from their enrichment experiences but playing well is not one of them.
Contrast that to beginners in a school band. They play sloppily. They don't articulate, they can't play in tune, they don't know all their fingerings, they miss accidentals - but they play on the beat. They practice playing without hesitations, while counting, and with the reinforcement of multiple others doing the same thing.
I may be overly sensitive to the hesitation problem. I am not "neurotypical," I have a slight brain function disorder, and timing errors are physically painful while wrong notes are merely annoying.
Almost everybody who picks up guitar succeeds. But most of their practice is playing along with music, being forced to play in good time.
It sounds like N has a strategy for dealing with the time problem in the early stages before the bad habits are fixed, or at least trying to.