Honestly, it's practice: it's even practice of the unusual demand to sit still and write when you don't feel like writing, about something you may not even be very interested in.
Children learn loads of things at school, including the seemingly weird practice of having to do things they may not particularly feel like doing, at times not of their choosing.
We're old and inured to it - but it is quite weird.
He'll learn.
In the meantime, incentivising at home, in little chunks, is the way to go.
The Class Teacher is going to have a whole structure of auditing and data pressuring her for visible results. Sad but true. She can't afford to have an able child in her class not producing visible, auditable results. And, for her, I guess it's also a behaviour and discipline issue.
That's the impetus for the sanction-driven approach she's taking.
It's probably worth saying that, in some schools, such an approach I. Year 1 would be a massive no-no. Some schools just don't permit withdrawal of play-time.
So it's probably worth taking a very different, rewards-based approach at home.
And it absolutely is worth talking to your son about why. The answers won't come quickly - it takes time. But he's the only one who knows.
It honestly could be anything. He might find the teacher a bit scary. He might just like day-dreaming, or talking to a friend. It really could be the child opposite him kicking him under the table.
My daughter started a new school and her maths went downhill. Turned out, it was a child on her table kicking her in class!!
He's very small.
And I've noticed that some children just don't settle down to writing/completing work until later. Then suddenly (end of year 4) it all goes 'bang' and suddenly they're on task. So it really can just be about maturing into the demands of school.
In the meantime, you have a bright child, who is learning. So you really can celebrate the positives, and smile about the fact you're doing OK as a parent.
(I'm guessing that part of all this is because it's making you question yourself as a parent. You don't need to. It's OK.)