whitebear -- to the first part, I agree LaEscopeta's comment is perfect.
(and I was wondering when the observation you posted would surface, actually).
More to the point though, the difference is not relative skill level*. The difference is
mission.
A domestic police force is tasked with preserving public order in a
civilian setting. There is no call for light machine guns in that role. A police force
must be more surgical in its response than the very
nature of a machine gun allows.
In contrast, civilian ownership of arms as covered under the 2A - as insurance to protect the liberties of the people against the dangers of a corrupt government and/or standing military - that is a
military function.
If God help us it ever came time to
use the 2A as the founders intended, then a LMG
would have a role in that mission.
(As would the military's Apaches, in taking out the owner of said LMG.
)
-K
* although I think we could probably agree that
on the average a firearms hobbyist will be better versed in arms than your average patrolman. Just as the average radio hobbyist will be better with a radio, your average car enthusiast may be a better high-speed driver, etc. Those who become specialists in a given avocation will often be better
within that skillset than those who must master it as but one part of much larger basic skillset for their job.