The 5th amendment specifically allows it for military trials, but for civilian trials, no, it's made impossible outside of cases where the defendant agrees to it by the 5th amendment.
Presumably, this is a big part of why Bush was so keen to relabel what had previously been considered civilian terrorists as military combatants, since the fifth amendment then apparently stops applying.
I don't understand the connection you're drawing between the 5th amendment and inquisitorial systems (which I understand to be jusics systems which do not separate the judgers of law (neutral) from fact gatherers (prosecutor)). The original comment above was about the no-self-incrination clause, and now you seem to say there's a tension with the grand juries clause. But I can't see how either conflicts with an iquisiorial system in principle (even if inquisitorial systems generally don't have grand juries in practice). Could you explain?
I'm getting way out of my depth here. My understanding has been, and seems to be corroborated by the Wikipedia article above, that the fifth amendments no-self-incrimination clause is usually interpreted in the context of an inquisitorial system - specifically the way the inquisitorial method was applied at Star Chamber.
IANAL, but the way I understand it is something like: You are a court, and you're trying to determine how the 5th amendment applies in some tricky case. The text itself might be ambiguous or unspecific in your case.
One way to approach that ambiguity is to look at the history of the amendment - why was it written, and given that, what is the most likely intended way to read it?
For the 5th amendment, the context is that the Court of Star Chamber used the inquisitive method, combining the search for truth with the force a court is able to apply to a defendant. In doing so, the Court of Star Chamber highlighted a flaw in the inquisitive method: Combining the right to apply force to its subjects with the job of determining truth created incentive for extensive abuse, as the court forced false testimonies out of its subjects.
Hence, the 5th amendments no-self-incrimination clause can be interpreted to exist to weaken the inquisitorial method in US courts, reinforcing the US commitment to an adversarial system instead.
But the police practice of collecting evidence (e.g. tricking people into giving confessions) seems completely at odds with their neutral investigator role inquisitorial justice.
The judicial branch is meant to be neutral judges - but police and prosecutors are not part of the judicial branch. In the case of prosecutors, their job is explicitly to not be neutral.
However, the 5th amendment applies there as well - they can't force you to self-incriminate, you are free to remain silent in police interrogation. However, there's nothing in the 5th amendment saying the police or courts can't ask clever questions - if you incriminate yourself because a police asked a sneaky question in interrogation, that's on you.
But the judge isn't free to make their own investigations, and the police are part of the prosecuting apparatus. So they evidence presented is biased, and the system is adversarial not inquisitorial.
Sneaky questions versus outright lying? From what I've read, that's common practice for US police officers in suspect interviews.
Presumably, this is a big part of why Bush was so keen to relabel what had previously been considered civilian terrorists as military combatants, since the fifth amendment then apparently stops applying.