But the Swiss do it. At least in the schools of one canton they do. As a recent report in this newspaper on a parliamentary visit to that country pointed out: "Zurich canton, visited last week by the select committee, has no headteachers or secretaries - or schools. The basic unit of education is the classroom."
So if schools, why not colleges? We might think the Swiss a bit on the finicky side when it comes to cleanliness, but they manage to spend twice as much on education as us Brits and pay their teachers more than any other country in Europe, so they must have something going for them.
Of course to abolish both heads and schools they have to run a totally different system to ours. To quote again from The TES article: "Many administrative procedures seen in this country are simply not done or are carried out by the local education office."
And in place of heads, "...classroom teachers vote for a leader, a first among equals, to represent them with the school board, the employer." Now there's an idea: a head who is elected by his or her underlings...
But back to reality. Before we start sharpening the knives too vigorously, perhaps we should first consider what it is that college principals do.
Students have a refreshing take on this. If you spend your life working within a hierarchy you inevitably view it as a "top-down" system. But for the students, it's bottom up. They see only the teachers and what they may (or may not) do for them. Anyone else in the set-up needs to justify their existence.
Thus their view of the average principal's life can be summed up as follows:
* they wear suits * they sit in meetings all day lthey push paper * they appear, like royals, only on ceremonial occasions and for the rest of the time they indulge in non-stop gourmandising and other acts of high living at the taxpayer's expense.
Of course us lecturers do our best to try to counter such distorted views - portraying our leaders at all times as possessing the selflessness of St Francis combined with the workaholic habits of a Margaret Thatcher - a sort of St Margaret of Assisi if you like.
But then we have our own perspectives too. These days we tend to see principals rather as inquisition victims might once have viewed their torturers - not exactly as the instigators of the pain, more just the instrument that is used: "I really don't want to do this. You realise it is hurting me as much as it is you..."
We watch as they first draw up their five-year plans and then shoehorn them down into three when the current orthodoxy states that three, not five, is now the thing.
Indeed chasing orthodoxies and then implementing them seem to us to be one of their main tasks.
Inevitably this will mean restructuring the entire college at least once every six months (with attendant sackings) as they struggle to fit the proverbial quart into the pint pot that is their budget.
What their employers think that principals do - or should be doing- can perhaps best be judged by the way they seek to appoint a new one.
A recent advert for a small rural college asked for three things from their prospective top dog: leadership, development and strengthening of courses. "No more than a day's work there then," scoffed a colleague I showed it to.
The full job description, which by sleight of hand appeared on my desk some days later, showed how the rest of the week would be spent. Those strategic plans played a big part; as did liaising with external bodies. There was quite a lot too about money: how to get more of it and then how to dispense it with the greatest of parsimony. In around 300 words of text the word "student" appeared once and "students" twice.
Reading all these, particularly the bits about principals fitting their colleges into the bigger picture, might give us pause to think about some of the practical difficulties of abolition. Maybe there are just too many other things to abolish first.
But even so, can't we still learn something from those canny Swiss? Because doesn't their emphasis on the classroom as the foundation on which all the other paraphernalia of learning is built remind us of what education, further to otherwise, should really be about? As our students tell us, not so much top down as bottom up.
Stephen Jones is a lecturer at a London FE college