If you spent six months grinding the ISK to buy and outfit a carrier, how willing would you be to take it into a battle where any of a hundred things could destroy it, including server lag or a random disconnection?

I would invert the causality. Why would I spend six months outfitting a carrier if I had no intention of using it in combat or even flying it anywhere where other people would see it?

Same reason people spend hours tending their farmville farms...

I've never played Farmville, so I probably shouldn't speculate, but I'm under the impression that it is at least ostensibly a social game where you invite people to help with or at least view your farm.

Yeah, but so is EVE and other games like it. I have never played EVE for any significant amount of time, but I did play WoW for awhile and there were tons of things that people would sink time into for purely social reasons. I imagine EVE is the same way. You don't just want a Titan because it is useful in the game, you want a Titan so you can have a Titan.

It's more of a social ponzi scheme. The fun part is the very-passive, easy progress. You just click on things. When you get people to participate in your farm, you're just saving yourself lots of time and clicks.

Well, you wouldn't do it at all. That's why the alliances try to help their members after fights.

Maybe you just want to use it to pick off all the smaller guys. You enjoy driving it around and being the Big Man On Campus. But, you don't want to take it into a real fight, you might avoid an actual conflict with it.

Whipping it out when there's a major battle going on, becoming the star and centerpiece (or one of them) of it, :p.

Strategy isn't just about throwing everything out as soon as it's created and ready to go pew-pew.

In the words of the Lord, our Saviour, Mr Robert Downey JR...

"Peace means having a bigger stick than the other guy"

Alliances accumulate supercapital fleets so they can fly their collections around with relative impunity. Of course it tends to be awful for everyone who doesn't get to be in the big fleet - as they rarely get to play. This leads to the congregation of supercapital pilots in the same alliances.

Pandemic Legion is famous for this - as they have long had the biggest fleet, used it the most, and thus attracted large numbers of other supercap pilots. But they do not hold space.

And to correct a seemingly prevalent misconception - most titans and supercarriers are personal possessions. There are some alliance/corp owned ones - but the majority are simply owned by long time players who either botted (completely un-policed for a very very long time), scammed, traded, speculated, Wormhole'd or Ratted/missioned (Oh god please no - boring monotonous PvE in the extreme for low returns) their way to 80b isk fortunes.