Alexander Hamilton was an elitist, who didn't really care about the rights of the average citizen, so that would be his view. Instead, I'm with Jefferson on this one; a Bill of Rights was necessary to draw a line that governments couldn't cross. Without it, the U.S. would probably look similar to Europe with its disdain for individual rights. Some of European laws, especially the ones banning "hate speech" and individual religious expression, would be struck down as unconstitutional in America.
Numerous clever and learned analysts have pointed to the fact that the Bill of Right focuses almost exclusively on abuses best known to have occurred in the reign of Louis XIV.
Obviously the targeted audience were the hundreds of thousands of descendants of French Huguenots then living in the United States.
From what I've read of Hamilton, I'd have to disagree. His argument was that the federal government should be so limited in authority and power by the Constitution that specifying protected rights would be redundant and unnecessary. If the Constitution does not grant the government authority to regulate speech and press, then there is no need to explicitly protect them from the government, because they are restricted from anything outside their Constitutional authority.
The Constitution was created with the attitude of "The government may not do anything except what we explicitly give it authority to do." The Bill of Rights takes the opposite approach: "Here is a list of things the government cannot do.", which necessarily implies that anything not on that list of prohibitions is fair game.
I tend to agree with Hamilton's approach. The default position of the Federal Government should be, "That's none of our business." Only those powers granted by the Constitution should be ever entertained by our elected representation in Washington. Everything else is strictly off limits, specifically granted to the states for their consideration.