I remember having the Plasma Pistol as tool of destruction during a random co-op campaign legendary game on Exodus, I was simply running with it and Magnum then DMR for ranged/headshot attacks, until the last part where I usually gather a lot of Fuel Rod Gun ammo (usually goes unused, better to rush the Wraith near the bridge) .
Shielded Brutes aside, you can own everything else with the Plasma Pistol in that mission, facing Brutes head-on with little fear of dying is a thing, the stun let you add even more damage.
But I wouldn't try this on Elites, being the opposite of Combat Evolved, flinching animations are very short for them.
The Plasma Repeater is the counterpart to the Assault Rifle, no pratical reason to use it when the latter can do some long range killing. The Plasma Rifle have no excuse, I feel it is less powerful than a Plasma Pistol and accuracy is a bit too wild for me, also not super common like it's repeater cousin.