We're discussing conceptual theories, not their ideal applications, fake-it. Whether it is implemented in perfect fullness or not, the term "capitalism" in the modern sense refers to something of a laissez-faire persuasion that at the very most only tolerates intervention while arguing against it. It does not refer to that which celebrates and openly espouses intervention as a positive good as Hamilton did. The two are mutually exclusive.
Ayn Rand is not an economic thinker of high quality or historian.
Who ever brought her into it?
Hamilton's ideas went far beyond mercantilism
Every economic historian whose worth anything identifies Hamilton as a "neo-mercantilist" and places him in the same school of thought as Freidrich List. I've already given you dozens of references to this universally accepted fact in our previous debates. That your bizarre Hamilton fetish induces you to reject this notion and buck the entire field of economic sciences is not a concern to me as your unsupported personal opinion carries no weight with much of anything.
Laissez faire is a nice idea but impossible in a political world particularly a democratic one. Hamilton dealt in realities and practical applications and demostrated quite handily that government intervention can be very productive. He never said or wished that the government should control the economy. It could be a positive good but was not necessarily so. His assumption and funding program showed that it was such in that case.
Capitalism, the Unknown Ideal brought her into it since it postulated the same thinking you employ.
Your evidence of Hamilton's mercantilism is essentially trying to use a revenue tariff as evidence of a protective tariff which I rejected. Hamilton's ideas wrt economic change went far beyond anything Mercantilism ever proposed.
Nor does acknowledgement of this fact buck "the entire field of economic sciences." In fact, reducing Hamiltonianism to mercantilism indicates you don't understand either.