You can't have Martial law without either police, military, or National Guard to enforce it. You've shut down everything but hospitals so who is going to be delivering these military rations? What you are suggesting would cause widespread panic, looting and chaos in general.
I do agree the list of "Essential" businesses is a little on the lax side. That should be tightened up. Anyone that loses their jobs, even if just temporary, should be immediately eligible for unemployment benefits too.
If you have martial law, that goes without saying that the military will be there to enforce it. Also, martial law is the suspension of civilian law, so theoretically local law enforcement will have 0 authority at that time.
All we have right now is organized chaos and widespread panic. People just haven't gotten the nerve to start looting yet. Have you seen the grocery stores lately? Now imagine we have 1 million people infected with COVID-19. A lot won't even be presenting symptoms at the beginning. They are still allowed to go out to the grocery stores and banks and what not. Spreading the virus around, even though they are doing only the essential. A stay at home full lockdown is the only way we can go about it unless we want to drag this out for months. Or resume life as normal and have a Darwin effect. Otherwise, we are crippling mass amounts of people due to economic reasons, and most won't recover.