Freedom is the ability to make choices, which means having the power to choose. Great power is a great freedom in choices- and of course that freedom comes with a responsibility- you made choices, you are responsible for them.

And yes, if you have no freedom you cannot be considered responsible for what you do or don't. A slave cannot be held responsible for actions he's been ordered to perform. This might not be "blissful carelessness" but certainly is lack of responsibility.

that implies there 's a tradeoff between freedom and responsibility. freedom is a natural right - responsibility, while highly valued, is not required.

We are simply confusing two different meanings of "responsibility" and misunderstanding each other.

Responsibility is both a way of acting that is mindful of the consequences, and simply the fact that people will ask you to respond of the consequences of your actions.

The two are strictly connected but are not the same. You "act responsibly" when you are prepared to answer tough questions about your actions. The simple fact that you will be asked to answer those questions, independently from your actions, is the fact of "being responsible".

So responsibility as virtue is not required by freedom; but as a simple fact of life it is its consequence, people will consider you responsible for what you do.