First, I disagree with your notion of "specific welfare", finding that to be mincing words. Thomas Jefferson wrote at length about the importance of an educated population and how that was one of the few things that guaranteed self-governance. He went on to say that there are too many instances of families who could not afford higher education for their children nor had they the time, patience, or faculties to educate their children. He proposed bills numerous times in Virginia in order to establish public schools.
Food does not bring an education, yet an education can certainly bring food. Healthcare will not bring education, but and education will bring healthcare. In keeping with the general welfare, it is prudent to fund whatever provides the best leverage for all people at the lowest cost. Education is an enabler, unlike those you list.
The limited culture of the government did not escape me, I can assure you. Yet, the Constitution does empower Congress to make laws that are not prohibited. If Congress were restricted to making only laws included in the Constitution's enumeration, it would not have seemed necessary to include the Bill of Rights. After all, how could anything in the enumeration of powers affect the possession of firearms or the free exercise of religion? It seems pretty clear to me that lawmaking in general was expected to go outside of the enumerated powers so the phrases I highlighted really are general purpose in nature. (They wrote more compactly in those days.)
I clearly see my viewpoint enumerated in the whole block. You are taking a stance that is similar to the way people want to tie both clauses of the Second Amendment together when they claim it empowers only a national guard.
The Founders did not list at lot of things in the enumeration of powers, just like they omitted quite a lot from the Bill of Rights. There was a great deal of debate about these very things. They finally concluded that nobody would forget the sting of tyranny, and that the states were going to cover everything else anyway. Of course, the states were assumed to be the seat of power when they wrote the Constitution.
Sure enough, schools are established by the Constitutions of all fifty states, not the Federal government.
"Sure enough, schools are established by the Constitutions of all fifty states, not the Federal government."
I fear this use of the word "established" the way you have been deploying it is set up to contain a back door. There isn't an enumeration for schools in the enumerated powers of Article I Section 8. That is simple and clear cut.
But what about a back door technicality, where as long as the states "establish" the schools but then the dictatorship comes in and makes all the rules and does all the heavy lifting and conducts day to day business?
No. This still is not the United States Constitution. There is no such back door. The lack of an enumeration does not just mean that the feds cannot establish schools, it means they have no role whatsoever in the fullest extent that the word whatsoever contains. So then the use of the word "established" as quoted above is unnecessary and perhaps even unwarranted.
As far as the United States Constitution is concerned, coming out of the Constitutional Convention in 1787 what we were given is a wall of separation between education and state.
"You are taking a stance that is similar to the way people want to tie both clauses of the Second Amendment together when they claim it empowers only a national guard."
Far from it. The history and the revisions of 2a until it's final wording make it clear that those folks have it wrong. Likewise, Madison's notes make it clear that we were not given a social constitution. The states, do, however have social constitutions. At least partly. The state ratification debates again confirm this.
One of the most remarkable days of the Constitutional Convention in this regard is July 17th, 1787, where you can nearly see a fist fight occur within the pages. https://avalon.law.yale.edu/18th_century/debates_717.asp The more and more they debate here on the 17th, the more agitated they clearly get. It's impossible to miss. There are other days as well that highlight how the Founders wanted to keep the federal government in a box domestically, but this day remarkably drives the point home.
During the Convention, and again, throughout the Federalist Papers, the vast majority of the time the Founders refer to the new government as a "general" government. Not a centralized government. Not a nationalized government. As they say in July 17th, the Founders did not want the federal government "intermeddling with their police" - that is, whatever it is the states were doing.
During the Convention, there were Founders who wanted to abolish the states and make America "one big nation". They were resoundingly defeated. There was another proposal that the Feds should be able to negate (veto) acts of the states. This also went down in flames.
We do not have a centralized government. We do not have a national government. We have a general government. The fact that it is only a general government and nothing more is incredibly significant.
A national or a central government would be able to do schools. But not a general one of incredibly limited means.