Which is why a purely market economy, which relies entirely on the mechanisms you describe, would be shit to live in. It's about the price of everything and value of none.
Not the case. It is about each person contributing what he/she is able. Free market economies only fail through Government intervention in the market.
In an actual nation, of people living together in a society, there are social and ethical ends as well as monetary ones. Which ever flavour of economy you choose, it's a means to those ends. Where an economy doesn't serve the need of the nation, it gets steered and curbed till it does - eg with monopolies regulation, to prevent the free market economy reaching its natural conclusion of monopoly.
Again, a fallacy. Monopolies cannot develop in a free market economy, because there will always be competition. Monopolies only develop because Governments intervene and the free markets to favour one company over another, or to legislate in favour of one group over another. If you left individuals to decide freely how they wished to spend their money, in a free trading market, the markets prevent monopolisation of goods and services.
The individuals who do best financially in a partially free economy are those who value their own labour according to purely monetary and utility arguments, and other people's labour according to social and public good arguments.
And this is not borne out by history. We live in a far less generous and charitable age than at any point in our country's history. We have seen far greater depreciation of people's wealth in the past forty years than in the preceding 260 years. It is crony capitalism, an economy where the government legislated and manipulates economics that destroys job markets and businesses. Not a free market. We have not operated a free market in the United Kingdom now for going on 150 years.
Otherwise, under value-based pricing, they'd have to sign their house over to the paramedic and nurse who save their toddler's life...
That is laughable. You are comparing crony capitalism to some ideal socialist utopia that cannot physically exist in real life. You do not seem to understand what a free market economy is or how it works. What you see around you today IS NOT a free market economy. Nor is it a democracy. The fact that you may think it is either, or both, is a testament to the effectiveness of state education.