Even though I'm disturbed and freaked out by the kissy smiley..

The only time I dock them is when they've gotten so beaten up that they're mostly ineffective (like if you only have 1-2 fighters left out of a squad). Docking them keeps them safe while they rebuild, because otherwise you'd just keep losing the one measly fighter over and over while fighting and the squad won't replenish until the battle is done.

This is only really useful early on when you don't have 50+ squads zipping about, though. Then you just tend to not care about single squads much.

Conceivably, there are some capital ship abilities that make life rather hellish for strike craft but the AI doesn't really use them much (and I don't play MP) so even though docking would spare the craft until those capitals are done, I never had to do it.

It's useful if you have a carrier-heavy force and you end up being confronted with a flak-heavy force.  Then you just want to dock your strikecraft and get the hell out - your enemy has you countered.  Also can be used when you want to make a quick phase jump out of the system.  Normally you have to wait for all your strikecraft to fly over and dock.  But if you dock them while on your way to the phase lane, there is nothing left to dock once you arrive, and you can just go ahead and jump.

Strike craft do attempt to return, but if the carrier departs first, then the strike craft are magically sucked into the carrier's hangar bay and released when phase jump is complete.

Its fairly obvious when you're in an uncolonizable well with enemy trade ships or scouts regularly jumping in. Strike craft can't resist targeting these guys (unless you've specifically told them not to by turning off auto-attack or set engagement ranges to local/hold) so its entirely possible that a squadron is on the opposite side of the well when the carrier begins charging its phase drive.

To me, it looks retarded to have fighters always outside the carrier. The people piloting those fighters must get tired. And the fighters must wear down mechanically. It would make a lot of sense to keep them stationed inside the carrier unless an enemy is nearby.

In fact, I don't understand why sins keeps the fighters and bombers outside. Why aren't they automatically docked unless you ask them to undock or an enemy is near by? That makes much more sense.

Well, Advent strikecraft are drones so pilots getting tired is not a problem for them. 

early in the game I tend to use the dock mechanism when you're coming to a planet with 2-3 flak frigate privateers, I'll then keep 1 out and play cat and mouse with the flaks, while the rest of my ships destroy their mates, then recall and pound the flaks dead

Docking your strikecraft manually can also let you phase jump faster since your carrier's won't jump unless your strikecraft are docked. It will only save you a few seconds, but maybe that could make a difference.