Good point. I'll think more on this.
One thing though which makes this non-obvious: We are in an equibrium system where demand and supply rebalancing change things. Economic utility and purchasing power of $1000 is the same whether someone earns $10K or $10MM per month. For somplicity sake, if all are made to pay $30,000 per year in income taxes, those who earn less would stop working, however, the demand-supply rebalance would either raise their income levels or the industry would have a higher drive for innovating and inventing to automate those jobs. In a similar fashion, with lesser taxes for the super-riches, more people would incline towards doing startups, etc. When that rebalancing is considered, the point of equalizing pain does not remain obvious to me anymore, as of now. :-)
>> Taxes are not proportional to income. We have marginal tax rates, not all-income tax rates.
Yes, I had made an approximation when writing "proportional". Marginal tax rates makes the income taxes grow faster than proportional with the income, whereas I am arguing for a constant income tax. :-)
Marginal utility of the $1k is not independent of income, even if purchasing power (almost irrelevant in this context) is. This is just basic economics.
> more people would incline towards doing startups, etc.
This seems naive. The rich do not, in general, do startups. The super-rich in particular do not do startups. Maybe you mean "invest in startups", which is an entirely different thing, since it presupposes the existence of startups to invest in. There is zero evidence from anywhere in the world that reducing taxation on the super rich results in any notable increase in investment activity.
I have no idea what this "rebalancing" that you're referring to is. I see no evidence that economies in the real world are in equilibrium states, nor any reason to suppose that they would be.
> For somplicity sake, if all are made to pay $30,000 per year in income taxes, those who earn less would stop working,
This thought experiment seems fairly pointless. This isn't going to happen. And if it did happen, people would not stop working. People need to eat, etc. Depending on the enforcement of the tax, they would have to find more or less ingenious evasion methods.
The fundamental model behind progressive taxation is that the pain of paying taxes should be roughly the same regardless of income level. The notion of "pain" in this context is closely tied into the concept of marginal utility of income: how much value does a given person get from receiving an extra $X in income (or conversely, how much do they lose by not having $X in income). Give an extra $1000 to person who only earns $12k/yr, and it's a pretty big impact. Given an extra $1000 to a person who earn $12M/yr and its just noise. Taxes follow the same principle, but in reverse. When we tax those with very high incomes, we want them to feel the same "pain" of taxes as those with lower incomes. Because of marginal utility, that requires different marginal tax rates.
> the very premise of taxes being proportional to income has flaws.
Taxes are not proportional to income. We have marginal tax rates, not all-income tax rates. Someone who earns $40k/yr pays the same taxes on the first (and only) $40k (likely close to zero) as someone who earns $4M/yr. Someone who earns $200k/yr pays the same taxes on that $200k as the person who earns $200M/yr.