The amazing Lucy Kellaway, former Financial Times journalist and founder of Now Teach, has reached the conclusion that teaching is “unendurably hard”. Why, she asks, can’t we engineer things so that teachers can work three-day weeks? Having achieved that change herself, after her full-time training year, she’s now loving her job – and is, I’m sure, a better teacher for it.

I admire Lucy and would love to meet her. Her widely-shared experience has shone a spotlight on the harsh realities of teaching. What follows isn’t intended as criticism, merely comment on the unanswerable questions she raises.

On one level you can’t argue: most teachers would cope better with a three-day week. They’d be less exhausted, escaping from the marking-preparation-and-admin treadmill and, hey, be allowed a life.

The first problem is financial. Most ordinary teachers would struggle on three-fifths of a £25K salary. By contrast, in her revealing BBC Radio 4 series, aired in the summer, Lucy quoted a Now Teach colleague who took a 90 per cent pay cut to follow her lead: she had similarly left a highly-paid job.

Of course, the genius of Now Teach lies in recruiting such people. It’s right that government, now clutching at straws when it comes to teacher supply, has agreed to fund it – though you might argue that, at £10.7m, the straw is a costly one.

Next, schools have always been grateful to recruit experienced part-time teachers, but could they operate with a majority of part-timers? The difficulty is not so much about constructing a timetable around fragmented staff availability (though that shouldn’t be underestimated) as about giving children continuity.

This year Lucy Kellaway has changed subject, now she teaches economics and business studies. I suspect those will be offered as options, only at the top end of secondary, so her pupils will cope with not seeing her on two days in the week. By contrast, it’s widely felt that younger children – 11 to 13-year-olds, say – best learn maths (which Lucy taught last year) through frequent lessons, absorbing and practising the vital basic principles, preferably on a daily basis.

So, if teachers taught three days a week, would pupils have to share two teachers in core subjects? How good would planning and liaison have to be to achieve effective team-teaching? Superhuman, if you ask me.

Besides, though I might stand accused of harbouring a sentimental, old-fashioned view of teaching, I’ve always seen the teacher’s role as much broader than merely “delivering” a subject (I hate that verb). The best teachers – those empathetic, approachable professionals who run tightly-organised and positive classrooms – have always been the first resort for children who are worried, lost or distressed.

A recent survey demonstrated, yet again, that teachers are among the most trusted members of society, and are thus heavily relied on by children and parents. Even supported by good non-teaching pastoral staff (we’ve seen them sacrificed to swingeing funding cuts in BBC2’s current fly-on-the-wall series, School), it’s the teacher whom pupils see every day and to whom they naturally go when in need. In an adequately-funded system, teachers would perform those traditional pastoral roles as well as teaching, and they’d be given sufficient time out of the classroom to do it.

It comes back, as ever, to the workload with which teachers are burdened – unendurable, says Lucy Kellaway, and damaging to their mental health according to a study by the Anna Freud National Centre for Children and Families. If Lucy’s right that teachers can only cope with three days’ work, then society is requiring too much of them, and should stop.

The government has a moral obligation to recruit and retain sufficient teachers to allow them to teach their specialism, give additional time for the pastoral and extracurricular work that were so long a strength of our system, and do it all without killing themselves – indeed, to render the job not just endurable but enjoyable and rewarding.

With due respect to Lucy’s observation, it’s the nature of the job, not the nature of the contract, that needs a fundamental redesign.

Dr Bernard Trafford is a writer, educationalist, musician and former independent school headteacher. He tweets at @bernardtrafford