I'm not understanding your point and the relevance. Its clear costs have to be considered and costs are related to the quality of the product or service. The NHS has always been underfunded, has always been considered not as good as it should be. The point is most would rather have a poor NHS than no NHS. There is always going to be a balancing act between taxation and budgets.
btw - I dont accept that bugest should be totally dependant on taxation. Costs can be cut, efficiencies made, preferential regulations. incentives, restrictions and the service can get additional revenue sources.
The difference between public and private sectors needs little discussion. But this where you lose me. You are applying private sector thinking and factors to the public sector as if no difference. Lets forget cost for a second. If education is accepted as public sector why should health not be. In principle, the concept, they are same.similar. If anything health is more important to the nation and people than education. Both can have public and private sectors.
The fundamental is one of principal. Some believe government should provide certain basics to the people. Defense, justice, education. health, food, shelter for the common good and the good of the nation. The cost -taxation - funding - quality question comes after the commitment to the concept that government should consider basic health a governmental responsibilty.
If you want to make the argument about debt then lets look at government spending as a whole and ask ourselves would we rather government spent trillions on making the lives of people in another country worse and shorter by bombing the crap out of them or making the lives of its citizens longer and better by providing health care.