I can think of three reasons, from least to most libertarian:

1) You're proposing a flat dollar amount be paid as tax by every citizen. This will be most painfully felt by the poorest. What sort of society do you think this leads to?

2) The rich do employ a lot of people, whose education and safety were provided for by taxes. Then there's all those road and water networks they use to deliver goods to the markets they own, and the large amount of property and contracts they have that are enforced by the state. So yes, I do believe they use more government services than the average person.

3) Plenty of markets work that way: https://en.wikipedia.org/wiki/Price_discrimination Furthermore, in a market, the seller sets the price, and the buyer is free to take his business elsewhere. And there's plenty of countries to choose from - so why should government services be different?

"Do you think the top 1% of Americans consume significantly more government services than an average 1% of Americans?" They obviously do consume more of about everything, including government services. Have you compared the cost to government of several McMansions versus a small rental appartment? Policing cost in an affluent neighborhood? The cost of people flying very often versus not or almost not? Of a heavy SUV versus a humble small car? I'm not even touching other externalities like environmental cost...

"If not, why should consuming those services cost significantly more money?" One doesn't even need the "if not". This can be a perfectly valid political choice.

"It might feel right that rich people should pay more, but that's not how any other market works - why should government services be different?" Because government services are not "any other market". To illustrate that, one could also turn this around and ask "It might feel right that everyone should pay the same, but that's not how government services work. Why should private markets be different?".

Because taxes aren't about market services? We, society as a whole, benefit from things that we don't consume. I'm not making use of social security, medicare, food stamps, WIC, or CHIP right now, but it benefits me to not have destitute people. Property owners pay school taxes regardless of if they have children in school because a well educated society is beneficial to everyone. I didn't own a car for over a decade, but my taxes still paid for roads and car-centric infrastructure.

Moreover, I detest that we even got involved in the wars in the Middle East, and was a strong supporter of NOT retaliating after 9/11. My taxes still pay for them.

Taxes have absolutely nothing to do with a market.

Yes they do consume a lot more government services.

Whole branches of government are set up to protect property in any forms. Outside of life and limb protection, the rich consume property protection more. Land, IP, bank accounts, shares, options, buildings, boats, freight... the rich have it because their property rights are protected by the government.

Because they benefit more from the society our "expensive" government has created. If they want capitalism without government, move your business to Mexico. What's that? There's a massive divide between the have's and have-not's and you'd never be able to make a profit?

I guess those taxes aren't so bad.

Because society is not a market. Markets are artificial constructs that serve society. Not the other way around.