I'm a higher rate taxpayer and full-time lawyer, so you don't get to write off my opinion on the assumption that anyone who works would agree with you.
There is an astonishing lack of understanding in your post; so much so that it really is hard to believe you're ignorant rather than just goady. I think there is a good chance you're just on the wind up... but here goes my response anyway.
It costs the UK government £7,000 per year to educate a child in primary school, and £7,800 per year in secondary school. So, under your system, every person who has a child has to have £7,000 - £7,800 per year available to pay for that child's education. The median pre-tax wage in this country is £32,890, meaning the average worker with a child has to spend 21% of their income on the education of each of their children (and that's assuming the cost stays the same, which is unlikely in a system where all schools are private schools and thus required to be profit-making).
Then we have healthcare. The average cost per patient of healthcare in the UK is c.£3,500 per year. It more than doubles once a person is over eighty. And if, God forbid, you get cancer, the cost could be tens or even hundreds of thousands of pounds per year. The average annual cost of health insurance in the US converts to £6,689.49 per person, so that's another 20% of our median wage earner's salary gone, on healthcare for themselves and the education of their child alone. Already the costs they bear are significantly higher than their tax burden is under the current system, and we haven't even considered the upkeep of roads and infrastructure, their pension, payment of their share of the national debt (does this conveniently vanish in your scenario?), defence and transport.
In summary, the overwhelming majority of people in this country couldn't come close to being able to afford to privately fund the services they use, which are currently a joint burden among us all. A joint burden from which we ALL benefit, because having a healthy, educated population where most people are literate and have access to vaccines and other forms of community shielding healthcare benefits us all.
And perhaps you'll just smugly assert that people shouldn't have children, if they can't afford £11,000 a year to educate them and access healthcare, and I'm sure the natural consequence of your insane and dystopian vision of society is that far, far fewer people would have them. And then what would happen is the workforce would steadily disappear, as we wouldn't have enough young people growing up and becoming doctors, nurses, teachers, farmers, refuse collectors, scientists, software developers and hospitality workers.
Essential services, all of which depend on a large, skilled workforce would fail.
The economy would dramatically contract as there were fewer consumers, workers, entrepreneurs. Businesses would close without the workers and customers needed to keep them going.
Universities, research labs, skilled trades and cultural institutions all rely on apprenticeships, education and a steady supply of new workers, so these would also fail.
Even if a wealthy minority continued to have children, they would be too few to sustain a technologically complex civilisation, and complete societal collapse would inevitably follow.
Which part of this, specifically, is appealing to you?