There's one category I will say should be permitted to carry firearms without much thought – that would be Tactical EMS providers, who function with a municipal or regional SWAT/ERT team. They should be trained and meet qualification standards set by the team, and be permitted to at least carry sidearms for defense of themselves and other members of the team.
If it will be regular street providers, then who will they be? Will they self-select? Will the service say that only certain people should be able to carry? Will the service say that certain staff members (supervisors, for example) should carry firearms? What qualifications will be required? What laws apply? Does it change if the service is requiring providers to carry?
My personal opinion would be that the providers should self-select. Carrying a firearm is a heavy responsibility, and something that one really needs to think long and hard about before they do it. Forcing someone to do it isn't really a bright idea.
Many of us elect to carry firearms for self defense off-duty. Likely we would be the core individuals considering carry on duty.