Many sound arguments have been made why such a policy would be wise if it were in fact true, but in reality the premise of the question is largely mistaken.
While there's much discussion around the fraction of the tax burden which should be carried by the wealthiest taxpayers vs those merely a bit above median income, the clear reality is that the overwhelming fraction of the overall tax burden is carried by those in the upper 50% of income distribution, and only a tiny part is carried by those in the lower 50%.
Traditionally there have been non-degree jobs such as skilled trades (often in industries with strong unions) which could result in a solidly middle-class income, quite possibly well exceeding the national median income at the peak of a career. However, these have been rapidly vanishing over the past two generations - a comfortable family existence supported by a single non-degree career is now exceedingly rare.
In recent decades, there are fewer and fewer workers without college degrees whose incomes put them above median income and into a tax bracket where they are asked to contribute even as much as (never mind more than) a per-capita share of national expenditures. Even cutting government expenditures back drastically and removing anything remotely arguable as a "subsidy" would not really reduce taxes in the lower half of the income distribution by much. While lower income taxpayers are still very much taxpayers, in the sense of federal taxes they are not really subsidizing anyone else, but rather only paying a well below per-capita share towards what even the most barebones government would have to expend on the fact of having citizens and territory. (And that's as it should be - we have tax brackets for a reason).
A small and shrinking number of exceptions do exist, in the form of those who either from entrepreneurial efforts, or by holding surviving union style or skilled trade jobs do end up paying a higher than average share of taxes without a college degree. But they are rarities; and most would not recommend that their own children enter the workforce without a degree, because they see through their own experience how uncertain such a path has become.
In reality, the cost of higher education subsidies is overwhelmingly carried by medium to upper income workers with college degrees, and this is becoming more and more true every year.
(Things like local property taxes are payed by almost everyone - either directly or as a pass through from rent; but with rare exceptions of city-owned colleges these fund only primary/secondary education. Subsidies of higher education are mostly federal, and to a much smaller degree state. In the latter case there may be a limited input from flat - which is to say effectively regressive - sales taxes)