there is no duty of “cooperation”.
The uniform alone constitutes intimidation by authority.
Right to remain silent means just that, silence is a right of the individual.
A duty to speak could be construed as a duty to prove innocence. (see also duty to die for the public good)
We have many rights, the exercise of some of them may have consequences. For example, we have the right to free speech, but some speech may cost us in various ways, such as job opportunities or a lowered position in the eyes of some. I am free to practice my faith, and others are free to consider my faith evidence of my stupidity. It is a price that exercising freedoms can cost.
Keeping silent is our right; having others agree that in some circumstances that such silence doesn’t suggest culpability is not a right (or should not be, in my view). Defense counsel may be able to make a very good argument as to why the defendant has elected not to testify: he no longer recalls what happened; he has no evidence to offer because he was not anywhere near where the crime occurred (of course he could testify to that effect if he wished); he is too stupid to avoid being tricked to admit to something he did not do when being cross examined, etc.