Certainly they are superior at managing the patients.
I am not sure that is necessarily the goal of community paramedic programs, it is not the overall goal of ours at least. Our patients are still managed by their physicians/midlevels and we are just there as follow up. Do you take your meds? Have you had a medication reconciliation? Is your home suitable for your health status?
We play much more of a home health and resources navigation role than that of primary care. For our rural area, there is a shortage of both primary care and home health, but it is much more noticeable with home health. There is one agency for many hundreds of square miles and they are often unable or unwilling to see patients within a reasonable time frame. It's pretty low hanging fruit, but it really does help keep patients out of the hospital. It's not flashy and we aren't suturing or running around with iStats (though those are coming), but we've been able to effectively manage about ten "super users" in our system in the last year. It's not much, but over 2500 calls and two to three ambulances staffed a day, it does make an impact, and we can do it just as effectively as a mid-level can, it's just not complicated to roll up throw rugs or recommend the patient's room have a bathroom on the same floor.
We also do mental health evaluations and transports to a freestanding "psych ED," which with some extra training is more than reasonable for a a paramedic to be doing. Sure it would be nice to bring a case worker right to the scene but the money is not there for that. It is far cheaper to have a paramedic do basic POC testing and a flowchart assessment to see if the patient is appropriate for these sorts of facilities, where they will see a psych provider anyway.
TLDR; community paramedics doing home health is viable and does not require them to mimic the clinical accumen of higher credentialed providers. Perhaps we should be focusing our efforts on this rather than the more flashy "primary care in the patient's living room."