But that's what I'm saying -- you could, perfectly logically, have a middle ground between "You have the right to refuse to answer any question asked by the police" and "You have to answer any question asked by the police". You could just say, instead, "You have to answer any question about information you might have regarding the specific crime they're investigating, but you don't have to answer anything else that's irrelevant, and the burden of proof is on the police to show that something is relevant."
The standard would become "if the police ask the question it must be legitimate, otherwise why would they ask it", which is effectively the same as having no middle ground. Any challenge would necessarily have to happen post fact and would be difficult to prove.
In other words, make the rule the same as it is for third-party witnesses now: you can't be coerced into a giving a *particular* answer (and, obviously, can't be tortured or anything else like that), but you do have to answer questions about the actual crime. (And if the state thinks you're lying, they have to prove it beyond a reasonable doubt just like any other crime, of course.)
Third party witnesses can only be compelled to speak with a subpoena (in a court of law), otherwise retaining a right to remain silent. In court the attorneys and judge act as checks against each other so that improper questions can be dismissed (although it is not the person being questioned's decision on what is proper). So as for questioning by the police (as opposed to the courts), third-party witnesses have the same rights as a suspect.
As for why the dissimilarity, the Fifth Amendment was reactionary, and remains as a protection against a corrupt court (the most recent example being McCarthyism). Because third-party witnesses are generally not harmed by their testimony (unless they self-incriminate, and they can invoke the Fifth Amendment to prevent that), they were overlooked in protection.