Oh, Joe, all the things you don't know! Your claims are factually inaccurate; Internet patriots should censor these particular ones as dismisinfoganda. Other fact checkers have already pilloried your ignorance of these matters! You, or at least your speechwriters, should read a book, literally my One Nation Under Debt (McGraw Hill 2008). In it, and the copious sources cited therein, you will find that private individuals could, and did:
form their own military units, usually termed "Legions," that included artillery units. That of Charles Dabney of Virginia is discussed in my book based on primary source research that I conducted at the Virginia Museum of History and Culture and military histories include plenty of other examples.
organize and charter private militia units as nonprofit corporations. On 28 October 1801, for example, Thaddeus Rice, John Hastings, James Godfrey, Reuben Rice and others incorporated a private artillery company in St. Albans, Vermont (see pages 120-21 of that state's annual statutes to verify). On 3 November of the following year, 40 individuals did likewise in Shrewsbury, Rutland County (pps. 44-46). Other examples abound.