President (and Founding Father) Thomas Jefferson and his Secretary of State, James Madison (who wrote the commerce clause) used it to prohibit foreign trade in 1808 -- so that can't be right.
They also used it to prohibit the sale of alcohol to the Indian tribes in 1802. So it appears that the definition of "to regulate" also includes "to prohibit".
"regulation of commerce among the states was only to remedy one state restricting navigation of another states commerce."
That certainly was how the commerce clause was used initially, yes. But I see nothing in the wording of the commerce clause that limits Congress to only the remedy you mentioned. As I pointed out, the commerce clause was used early on to prohibit commerce.