arming a colony ship is a waste because the ship is destroyed after it's used. it's better to bring an escort that can turn into a defender, if the ship's death is really a threat at all.
i would arm miners (bad joke continuation alert) if i lived in the south, but also because even though they won't survive, they're sitting ducks anyway. i generally don't build miners early in the game, and often not well until mid-game when i can afford to research the mining line at a leisurely pace. by then, the extra cost in production isn't such a big deal. my only rationale is that, if they're going to destroy something i built anyway, i might as well do a few points of damage to them in the process.
if i'm building a 3-MA, i might arm my constructors while i'm building it, just to boost my military score in the short term.
i will often arm transports. if i find myself at a tech advantage but a population disadvantage, i'll often put 1 or sometimes 2 advanced troop modules on a medium hull and then deck it out with an engine, offenses and defenses. i don't intend them as front-line combat ships, but they can knock something out in a pinch, and because there aren't too many troops on any given ship, i don't invest large chunks of population on newly taken planets, not immediately anyway. after the war's over, leftover fighter-transports are put in orbit as defenders, also boosting population, leaving my front-line ships to do anything i might need them to (clean up pirates, fight other wars, or return to the center of the 3-MA "catapult" for rapid deployment).
as a nasty bonus trick, towards the later parts of the game sometimes i'll sell them to some AI who'll need to move them through another AI's territory to get them home... triggering a war.