Poor service is no argument against choice
Suppose that instead of the market in plumbing, there was only a state monopoly which also provided an inadequate service. Next time Professor Barber has a plumbing problem, he would still have to use the state service, even though he knows that service will be unsatisfactory. This is where the power of choice comes in: in the market, he does not have to use Deadcert plumbers ever again. And the likelihood is that Deadcert plumbers will soon be out of business.
The same arguments apply to a private monopoly. However, I think it exceedingly unlikely, because of the technological requirements of plumbing, that a private monopoly could ever emerge. Similar considerations about the technology and nature of education militate against a monopoly supplier.
On New Year's Eve I was travelling on a private Adirondack Trailways bus from New York to Montreal. Half-way there, the driver disappeared. After an hour and a half, the bus manager appeared, apologised ("it's New Year's Eve"!), and said he would drive us to Montreal himself, adding that this was opportune for him as he'd never been there before! I vowed I would never complain about (pre-privatisation) British railways again. But I also vowed I would never travel by Adirondack Trailways again.
Research fellow University of Manchester