They're messy, smelly, need a fair bit of maintenance, can be unreliable if you don't treat them right, and have the annoying habit of blowing out when you walk under a waterfall. But they have one big advantage over electric lamps (which many cavers do use): an open flame illuminates the whole area around you, rather than the single small spot your head is pointing at. The flame might not look very bright in the above picture in bright sunlight, but it's plenty bright enough in the dark surroundings of a cave, or the garage with the lights switched off:
There are a couple of other advantages of carbide: the reaction generates heat, so you can use the generator as a handwarmer when you're sat around freezing your arse off at at the bottom of a big waterfall pitch, and on very long trips you can carry extra carbide with you and refill the generator underground when it runs out (that came in handy on the 24 hour sponsored cave we once did to raise funds for the club).
One of the things I've learned the hard way is how to tell when unused fuel is "worn out" from sitting around in the tin too long. If you try to use it on a caving trip, it will typically start off working OK, but before long the gas production will drop off and it'll cause endless trouble before dying altogether after a couple of hours. There is a backup electric lamp, but it tends to not get used very often, and if you don't remember to check it as part of your preparation routine you may discover that it has a flat battery or corroded terminals when you're at the bottom of a cave (something else I learned the hard way). It's generally a good idea to carry an ordinary torch as an extra backup for just that kind of eventuality. Hiking back from Bar Pot at night when only one member of the party had a working lamp and he kept skipping away into the distance was an experience I'd rather not repeat in a hurry.
Of the fuel I had in the tin, there's probably just enough for one trip that looks OK, and the rest was clearly worn out, so I'm using the crap stuff up now and will buy a fresh tin as soon as I can get to a caving supply shop. Edit: the crap stuff wasn't as bad as I thought - it actually lasted about four hours; less than the roughly seven hours I've had from an ideal run with fresh carbide, but more than the two hours I've had on a bad day with carbide that's been sat around in the bottom of a tin for a long time.