Why not?
You frequently read stories of postal workers, utility workers and other workers who are out and about frequently saving lives simply because they are in the right place at the right time.
Oh, and by the way it is a constitutional right.
But giving them the powers of a LEO would be another matter.
I asked a US Postal Inspector, if as with other Federal Law enforcement agents, they had to swear an oath to support and defend the Constitution.
He replied, "yes."
I Then asked him if that oath included my 2A rights?
I got no reply.