This is not true, becasue according to Alexander Hamilton the phrase General Welfare is as comprehensive as any which could be used and embraces a whole vast variety of particulars:
Alexander Hamilton, Report on Manufactures
5 Dec. 1791Papers 10:302–4
A Question has been made concerning the Constitutional right of the Government of the United States to apply this species of encouragement, but there is certainly no good foundation for such a question. The National Legislature has express authority “To lay and Collect taxes, duties, imposts and excises, to pay the debts and provide for the Common defence and general welfare” with no other qualifications than that "all duties, imposts and excises, shall be uniform throughout the United states, that no capitation or other direct tax shall be laid unless in proportion to numbers ascertained by a census or enumeration taken on the principles prescribed in the Constitution, and that “no tax or duty shall be laid on articles exported from any state.” These three qualifications excepted, the power to raise money is plenary, and indefinite; and the objects to which it may be appropriated are no less comprehensive, than the payment of the public debts and the providing for the common defence and “general Welfare.” The terms “general Welfare” were doubtless intended to signify more than was expressed or imported in those which Preceded; otherwise numerous exigencies incident to the affairs of a Nation would have been left without a provision. The phrase is as comprehensive as any that could have been used; because it was not fit that the constitutional authority of the Union, to appropriate its revenues shou’d have been restricted within narrower limits than the “General Welfare” and because this necessarily embraces a vast variety of particulars, which are susceptible neither of specification nor of definition.