One big point you miss is that to do otherwise basically assumes that silence=guilt. If you refuse to talk to the police, right now that's a protected right. If people didn't have 5th amendment protections, it would be a crime to refuse to be interviewed by the police about some crime you were suspected in, guilty or not. In the real world, people incriminate themselves all the time. It's the police's job to try to trick them into doing so. Confessions are the goal of police interviews with suspects. Giving police the power to threaten jail for merely not talking would pretty much allow them to jail anyone they wanted.
Historically, the 5th amendment is about something much larger and more sinister, the practice of using torture to extract forced confessions. This isn't necessarily some outlandish thing, it happens in more subtle ways every day. When the cops keep a junkie too stupid to lawyer up in an interview room for 12 hours, eventually they will say anything to get out of there, once the withdrawal really hits.
Regarding your other scenario, extending 5th amendment protections to third parties, there have been some limited cases of that, married couples for example. The idea behind there being a different standard for third parties is that a third party testimony is a lot more suspect than a confession from the suspect. The motivation to torture a confession out of a third party about some crime they weren't involved in is pretty low.