Are you saying there are no cases where delivery through the state is less efficient than doing it privately?

A small example but getting paracetamol on prescription is vastly more expensive than buying it over the counter

There are costs and downsides to running things through the state. The question is what will give the best outcome. Sometimes it's clearly better, sometimes it's clearly worse and sometimes it's not clear. I understand the current discussion to be: which form of tax gives better outcomes

In either system people can go to university without paying for it at the time when they go

Its also possible for the opposite to happen. With a graduate tax, the current system, the money is linked to the university education. If it comes from general taxation, funding for universities will compete with the NHS, other schooling, pensions etc. It could easily be squeezed

Of course. I believe that it is true to say that not everything that is beneficial for society is paid for by society. Lots of advances made by businesses are beneficial for society. Why is taxing everyone better than taxing those that received the education for university education?

Of course but there is a point where we draw the line. For example, the NHS doesn't pay for ever procedure. Society provides roads and buses but not cars to people. Where do we draw the line and why?

My comment was motivated by the thought that one can regret the convergence of the repayment threshold and the minimum wage without calling for free education. Free education is a way to get around it of course

His child can go anyways but might pay a higher tax rate in later life. A graduate tax seems a nice method to move the risk from the individual to society and it feels more progressive than also have the people pay for it that see no direct benefit from it.

I'm not sure uni should be free. You are right of course that it is beneficial for society but it is also highly beneficial for the individual. Asking everyone, e.g. your local bin man, to subsidies the education of quite well off people, doesn't seem like nessecarily the most progressive approach