The first problem with this is that people who don't want to put themselves at risk for medical or any other reasons won't be able to stay in because once their job opens most don't have a choice but to go back and put themselves at risk.
Second, people are already going out and many, if not most, are not being in any way responsible. you yourself are even deciding when you want to wear a mask and when you don't.
Third, the problem with a virus is that in order to stop it, it has to be a blanket decision. Doing it piece meal only means that you are constantly running around putting out fires in different areas as the virus moves from one place that is locked down, to the places that are not locked down. Unless the area that are not locked down close the boards of their parish/county to all outsiders the virus will spread there as well. Letting people make the decision for themselves is the same as doing nothing.
We don't let people decide if they should speed, run red lights, steal, assault, kill, etc. Why would we let people individually decide if they are going to spread a deadly disease?
Finally, part of the point was to stop hospitals from getting overwhelmed, and we are at that point right now in some places. But, if people continue to be irresponsible and open the way they have been, then we will be back at that risk point very quickly again. Except this time, it will be nearly impossible to get people to stay at home again and if they do it will be even worse for the economy than if we had stayed in lock down longer. And, a bunch more people are going to die.