Laser Pistol vs All Predecessors

If (as argued elsewhere) the Heavy Cannon is the best primary squad weapon at the very start of the game, what to do when the Laser Pistol is available?

Unfortunately I think the Laser Pistol is so powerful that it immediately displaces the Heavy Cannon as the primary combat weapon, and forces it into a support role. The Heavy Cannon will languish on the shelves, at least until much more heavily armoured enemies arrive on the scene.

As a support weapon its use will be restricted to clearing terrain (with AP and HE), and delivering explosive rounds (including against terrorists). On a terror mission, it might be partly restored to its earlier value to minimise "friendly fire" against civilians.

In pure firepower, the Laser Pistol is more powerful than any starting fired (but not launched or thrown) weapon, against all aliens except the Reaper. HC-HE and AC-HE are about 4 times more effective than Laser Pistols versus Reapers (and twice as effective as Laser Rifles, even). Otherwise, the Laser Pistol significantly exceeds the Heavy Cannon (and Auto Cannon, Rifle, and Pistol) in general-purpose firepower, and far exceeds it on versatility, weight, space, ammo, speed and flexibility.

The main drawback of the Laser Pistol is its poor accuracy, especially when used in continuous auto burst mode (as is optimum). For this reason it might be good to retain Heavy Cannon for situations when accuracy is critical, since the HC is the best sniper weapon (out of the starting weapons).