> In all criminal prosecutions, the accused shall enjoy the right [...] to have compulsory process for obtaining witnesses in his favor...

Further reading: http://en.wikipedia.org/wiki/Compulsory_Process_Clause

So the Constitution is fairly explicit that courts have the power to compel testimony. That's not to say that the power isn't be abused, or at least used in a fashion not originally intended. But given the directness of this statement of a court power, your arguments against are unconvincing, since they rely on interpretations that are as yet unproven (like the right to silence).

The courts are generally more empowered than normal government institutions, because they are only invoked when other rights (may) have already been violated. The pursuit of truth, and in particular the pursuit of innocence of an accused party, may occasionally trump individual civil liberties.