Does a Statue of Responsibility impose values on others? Yes. But only values that are necessary for society to function.
Democracy is designed to encourage freedom of religion, speech, belief, and life goals. However, this freedom depends on honesty. It depends on trust. It depends on us respecting each others' rights. Compassion alone does not protect others' rights. We must fulfill our duties: to our families, to our communities, to our country.
Liberty does not, and cannot, mean freedom from the consequences of our actions! If you steal or kill, you are punished. If you are intimate with someone, the girl can get pregnant. If you have children, you have a deep responsibility to take care of them.
Every action has natural consequences. Every choice has responsibilities. It's even true in physics and biology! You reap what you sow. Every action has an equal and opposite reaction.
If America continues its current route of avoiding responsibility in favor of freedom from consequences, then it will fall apart as surely as the Soviet Union did. We will take out debts with no intention of repaying them. We will have children with no intention of raising them. We will get jobs with no intention of producing the promised goods or services with good quality.
Hence, responsibility is the necessary counterpart for liberty, or the people of the United States of America will never achieve the unity envisioned by George Washington, Abraham Lincoln, and, I believe, by God.