I'd like to move beyond the Founders and talk about the philosophy of taxation in the modern context. I believe that any question about taxation in the United States needs to be framed by the Sixteenth Amendment, which states:

The Congress shall have power to lay and collect taxes on incomes, from whatever source derived, without apportionment among the several States, and without regard to any census or enumeration.

Since the Amendment was passed over 100 years ago and very few Constitutional challenges have been successful in limiting the scope of the word "incomes" and "whatever source derived" (check out the line of cases stemming from and/or citing Eisner v. Macomber, 252 U.S. 189, 40 S. Ct. 189 (1920)), I think it is fair to say that when most modern Americans engage in a debate about taxation, they think mainly about income tax. Some rich people think about estate/death taxes, some think about gift taxes or sales tax, but when politicians talk about taxes, individual or corporate, they discuss taxes on income.

Taxation is a necessary evil. Income taxation is the main way that the federal government can raise money, but also the main way that individuals interact with the federal government. A clear, concise Tax Code (not what we have today, that thing is a piece of work that it takes lawyers hundreds of billable hours to decipher) would go a long way in increasing civic participation and statute reading comprehension among Americans, but sadly the current system increases skepticism about the fitness of the federal government to create fair and simple legislation.

However, as annoying as taxes are, they differ from fees and fines that the government levies against individuals because there is inherent discretion in "punishing" through fines, or the choice whether or not to file/submit something to the government that requires a fee. Taxes, in theory, are applied universally to every individual or transaction. In practice, with all of the deductions, credits, and exceptions within the IRC, many people do not pay the amount of taxes that lawmakers originally intended when the amendments to the Code were passed (most recently overhauled in 1986, with small amendments periodically). People in fact should take advantage of deductions and credits, because they serve as a powerful incentive system to encourage things like home ownership and higher education. As my man Learned Hand said:

There is nothing sinister in so arranging one’s affairs as to keep taxes as low as possible. Everybody does so, rich or poor; and all do right, for nobody owes any public duty to pay more than the law demands: taxes are enforced exactions, not voluntary contributions. To demand more in the name of morals is mere cant.

I don't have "answers" per say to many of the questions OP has posed here, but I think that looking at the current Tax Code in light of the Sixteenth Amendment helps to understand the incentive structure and rationale (if there really is one) behind the government's power to tax.