Re: sub-panel jumper
The purpose in life of the ?ground? wire (properly called the ?Equipment Grounding Conductor,? or EGC) is to carry fault current directly back to the source. It will do nothing at all, unless and until a hot wire comes into contact with the case (or any external metal part). If there were no ground wire, then the next time a person touches the case, current will flow from hot, to case, to human hand, through human body, to floor, through dirt, to ground rod, through Grounding Electrode Conductor, and finally back to the source. It won?t be much current, since dirt is not a really good conductor. But it will be enough to ruin that human?s day.
The ground wire connects to the case (or other external metal part). If a hot wire were to contact the case, current will immediately flow from hot, to case, via EGC to ?ground bus? at the main panel, via main bonding jumper to the neutral (what you called, in correctly, the negative bar), and thus back to the source. The resistance of this path is so low that the current will be high enough to immediately trip the breaker, and terminate the event.
Now to address your question: What if you connected the ground bar to the neutral bar at a sub-panel? The hot wires carry current from the main panel to the sub-panel. Between the main panel and the sub-panel you will have two paths for current to return. One is along the neutral, and is the intended return path. But since the neutral and ground are connected at both ends, the EGC is in parallel with the neutral. Therefore, some of the current that should flow through the neutral will instead flow through the EGC. That means that any and all external metal parts (including, perhaps, even conduit) will carry current all the time. That is an electrocution waiting for its first victim to touch something metal.
If the neutral and ground are connected only at the main panel, this parallel path will not exist. The EGC, the conduits, and all other external metal parts will not carry current, except when they need to (i.e., to trip the breaker, in the event of a fault).
Does this answer your question?
P.S. Please consider dropping the phrase "negative bar" from your vocabulary. I suspect that no one else uses it, and that no one else will understand what you mean.
