The preamble, in this instance, ties specifically to an enumberated power of Congress in Art I, Sect 8:
Under the enumerated powers granted to Congress is this: “provide for the ...general Welfare of the United States”.
1st sentence, iirc.
Read that way we do not have a government of enumerated powers. Anything at all could fall under that, like Obamacare. They can’t “Promote the General Welfare” by doing anything other than exercising the powers they have been granted. It’s a restatement of why certain powers are being granted; the power to tax in the instance of Article I, Section 8. Reading things into the Constitution that aren’t there is how we got some really bad decisions.