+1 on this idea.
My MD character has some downtime during some hours, this can definitely allow room for those type of coroner calls. However most EMT's do not have the ability to store a body in an ambulance truck, it isn't scriptly possible. This can be a suggestion to change that as well and allow bodies to be stored in ambulances. If this were to get implemented without the ambulance truck change then only Supervisors in MD and above would only be able to take the bodies from the scene since the scout ambulance can hold bodies.
I HIGHLY recommend adding the storebody feature to the ambulance trucks.