The concept of the grand jury is to have the decision as to whether or not charges are filed in the hands of "the people" and not an individual. Ideally, it takes the power out of the prosecutor's hands to prevent abuse of that power. In my experience as someone who presented to grand juries for several years, the problem with the grand jury process these days in much the same as many parts of "the system," which is apathy of the citizens. People don't want to commit their time and effort to being a part of the grand jury. in my jurisdiction, it is a commitment for every Thursday for three months. Some employers won't allow that, Those who do don't want to do any work beyond sitting in the chair, listening, and voting. The vast majority are content to sit back, listen to what the prosecutor presents, and call it done.
on the issue of jeopardy attaching when the grand jury starts, I'd say that is not a good idea. Under the law now, jeopardy doesn't attach until the first witness is sworn in, or the jury is impaneled (depending on the jurisdiction and circumstances). I've presented a couple of cases where there the matter was "no billed." Additional investigation turned up additional evidence, and upon second presentation, an indictment was returned. Don't want to have a case considered legally dead because it was presented too soon, or have later important evidence found and it essentially be useless. Also, in order to enforce such a thing, you would have to remove the secrecy of the grand jury proceedings. Otherwise, how would you know if a case had or had not been presented to the grand jury. And, if you remove the secrecy, think about the problems in having grand jury investigations open as public record...A thorough background check would turn up that "John Smith was investigated by the grand jury several times for molesting the neighborhood dogs and cats.' That could be rather damning for Mr. Smith in his efforts to find a job.