And if the First Amendment is not applicabe to the States (by way of the Fourteenth Amendment), some states could have freedom of speech and press and other states could forbid private ownership of newspapers or make it illegal to criticize state officers.
That might be a big price to pay for this monument. ;-)
"the powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people." Amendment 10 would cover that.