I have to disagree on the use of chemlights for spelunking. I carried them when I was actively caving twenty years ago and found them quite reliable and useful. Considering that they have improved over this time, they are more consistent and last longer in storage, than they used to I think they have their uses.

My usual lighting plan was:
Carbide light with spare water, carbide and a spares kit. Strong light and a source of heat. One baby bottle of carbide and two of water gives you, in very rough terms, perhaps 36 hours of light. Less if run wide open. Generally too bright for anything but huge caverns. More if kept to a pinpoint.

One 2-C flashlight with an under-driven incandescent bulb to extend the run time, a 3v light using a 4.5v bulb and at least one set of spare batteries and bulb. Run time was about four hours per set of batteries. Before LED lights this was state of the art.

2- votive candles and several ways to light them. Heat and light. Run time roughly 6 hours per candle. Less run time, and much harder to keep lit, if there was a wind.

Three to seven milspec 12 hour green chemlights. These were used blind diving wet sumps, route markers in same or across open spots, placed in or near important steps or hand holds, used to mark drop offs and other hazards.

They were also quite handy as a backup. Coming out of a low spot or sump we were never quite sure the electric lights would work after being dunked. So it was common for the first through to activate a chemlight. This also provided a nice luminous beacon, and sometimes confirmation they made it to the other side, for the next one through. It also provided a reliable area light to get warmed up, dry out your carbide lamp and to test and work on the electric lights. You always wanted to know what you had left to work with before pushing on deeper and keep at least two-thirds of your resources for the return trip.

Chemlights are no more subject to failure or exhaustion than any other light. I wouldn't go spelunking with only chemlights. They don't provide any warmth. But then again I wouldn't go with just a flashlight or just a carbide light. there is safety in diversity and redundancy. In terms of weight, bulk and burn time they were more of a bargain than any flashlight. Even today, with krill lights and LED flashlights, they hold their own quite well. They have their strengths and weaknesses. As with everything else you have to play to their strengths and work around their weaknesses.

As long as they were rotated and used while fresh they worked fine. They were sometimes the only reliable light source. Even expensive dive lights often became unreliable after a few trips. They were also heavy and bulky for the light provided.

Experienced cavers practiced the practical skills of being able to dry out and relight a carbide headlamp by feel after it was dunked. I could completely disassemble, dewater, repair and replace all parts my flashlight by touch. We practiced getting candles lit while cold and wet and in complete darkness. But after we started using chemlights, other than practice and showing off, we never had any call to have to do it.

Cracking a chemlight was quick, easy and cost effective. It also helped calm inexperienced spelunkers. Being cold, wet, in a confined space that is completely dark causes some people to freak out. Go figure.

My favorite light for caving and terrain search is still a good carbide headlamp mounted on a climbing helmet. Loads of bright white light in a long running, fuel efficient, compact unit. A subject for another day.