Paramedics don't have the educational foundations to do the things mentioned. Having worked in more than one arena within health care (paramedic and PA) I don't know that EMS providers are necessarily the best people for the interventions that are mentioned. This isn't to say that paramedics can't do those things and more. As Ruff mentioned education is ridiculously poor. This lack of education is a significant barrier.
Many of the PAs I work with currently are former EMS providers. Several of them are current EMS providers outside of the ER setting where we work. PAs, and to some extent NPs with an EMS background, would be best suited to work in that community health role doing the things needed to help reduce ER overcrowding and all of the complications that arise from that.
Unfortunately, there are barriers to this as well. Who is going to pay for that PA to be out on the street? I guarantee I'm more expensive as a PA than I am as a paramedic. Will call volume change when people realize the "ER will come to them"? How long until that becomes overburdened? There are logistical issues involved, too, never mind the legal issues that need to be considered.
The EM group for whom I work has talked about doing a community medicine response with the local 911 providers (both BLS and ALS). There has been talk about putting PAs into a street provider role to start providing care outside of the ER. I'm fortunate to work for a group that employs the state ALS and BLS medical directors as well as the county medical directors who could help make this happen. I've volunteered my services as have several of my colleagues with EMS backgrounds. If anything comes of it I'll keep everyone posted.