Yes, but should we? Likewise, should we have a Department of Commerce? I do not think so.
"It's not just "genuine involvement" -- it's genuine involvement in things that the Constitution has mandated that the federal government regulate. If the Constitution says the feds have to deal with interstate commerce -- as it does -- then failing to do so would be to reject the rule of law in favor of a flexible, activist view of the Constitution."
The government has the power to regulate interstate commerce, but not the duty.
"The Congress shall have power... To regulate commerce with foreign nations, and among the several states, and with the Indian tribes..."
I think that government should minimize its regulation of interstate commerce, because the marketplace can perform better without social engineering and government bureaucracy clogging the gears of progress. I think that government should focus its efforts on protecting our rights, especially from threats against our right to life from current and potential foreign enemies.
"Then what is the reason? As I said, the federal government was never authorized to explore space."
I could have worded what I wrote a little better. The reason is not the second sentence: "It will benefit human beings, because humans benefit by the advancement of American interests, but that is not why we should or should not keep NASA." The reason is the first sentence: "NASA is a fine tool for research and development of space, which is now part of our national defense strategy." That is not a justification for the creation of NASA. But, it is a justification for retaining a trimmed-down version of it, if it is put under control of the military.
"If we want to conduct research on defense, we don't have to do it under the auspices of an organization with an extra-Constitutional mission."
And that is kind of what I am addressing in the sentence above. Just as an interstate highway system is kosher, due to the power to regulate interstate commerce, military-related research and development is kosher due to the power to provide for the common defense.