The limitations from the spending clause are one component of a constitutional system dedicated to the control of factions. But it is also necessary to insist, as a constitutional matter, that all taxes be flat, as yet another protection against the risks of redistribution through faction. This can be done through a consistent application of the Takings Clause.
Many people might be either aghast or amazed at so strong a claim. But in its short form, the argument runs as follows. There is, in principle, no watertight distinction between taxes and takings. With the latter, the government occupies property, for which it must pay compensation. With the former, it threatens to seize property, via a tax lien, if taxes are not paid. In both cases, the government is allowed to take so long as it supplies compensation.
With specific parcels of land, that is done through cash payments from the public treasury. With taxes, the benefits come in the form of (non-divisible) public goods. To be sure, it is impossible to supply exact equivalents between property taxed and benefit supplied. But without question, the flat tax gives the best first estimate, while limiting the power of Congress to use an explicit program of redistribution that can rip a nation apart.
The efforts of all branches of government to keep that understanding alive were more or less successful until the early part of the twentieth century, when progressive forces began to overwhelm the more pristine conception of Congressional powers. The Sixteenth Amendment, ratified in 1913, removed the requirement that income taxes be apportioned among the several states, and was widely understood to authorize the imposition of progressive taxation as well. The Maternity Act of 1921 relaxed matters on the spending side to allow for federal funding for maternity and child care.