If they're not that dangerous, then it should not be necessary to keep tabs on their every move, or at least not necessary in a permanent fashion. Most criminal offenses are trivial, minor, and committed by people who mature and age. What you're left with is a very small number of criminals who commit a lot of crime and do some of the really nasty bits who would need to be detained and monitored.

But that's what prisons are for. That system is sufficient without infringing on the regular civilian population.

We often hold no one responsible for violations of privacy and even explicit Constitutional rights of disfavored peoples (minorities, religious or ethnic, or criminals engaging in private consensual actions such as the distribution of narcotics and other vice crimes). By tacitly accepting these violations, we risk our own. Your initial statement implies that these devices should be implanted in anyone, and then if they turn out to be a serial killer for example, then and only then should they be used by the government to track them down and arrest them. My problem with this is that while it might be okay to use such a device (as we do with house arrest tracking bracelets) on released convicts or other probationary states of people who have been convicted of a criminal act, this is very different from using such a device to intrude on people suspected of a crime or who are simply considered undesirable by the broader society (criminal profiling wouldn't be that hard to do herein).

A second problem is that once the state and its various agents and agencies has the arbitrary ability to monitor people they will use it regardless of what ends you or I happen to approve of its ability to do so. It is possible to use such legal protections as warrants to safeguard privacy, but providing the state with the technical ability to do something will imply that it will want as few obstacles to exercising that power as possible. This is an acceptable risk to individual freedom. If the cost is a few people die or are accosted by criminal actors, so be it.

We are better off not having the state decide what criminal actions it can investigate us at random for, and it already possesses broad legal codes and interpretations therein to do so without having the ability to peer into our daily lives at a whim. I'd rather not give them the whim too. We already lack explicit legal interpretations and expectations of privacy for many of our internet communications and other modern technological actions, and the government at present is more than willing to exploit this lack of clarity (while demanding it for itself, as in the case of Wikileaks or police and other officials being recorded by private citizens).

You may wish to hold such reprehensible action accountable for this disparity, but it is not the legal regime we have at present. The legal regime we have now acts from a presumption that legal rights which are not enumerated are not protected and this puts privacy at jeopardy except in explicitly protected ways (search warrants and free speech).

So Americans DO have the right to privacy.

So I ask you again…. what's to stop them from doing so?

Why wouldn't/couldn't/shouldn't they? Just because government and its agents are not supposed to use a particular power that we have foolishly granted them does not mean that they will not on the count that we do not wish them to do so only when it inconveniences us (and not when it conveniences our ridiculous demands for public order or safety).