I make very late call outs. My thinking is: something is either bad but not so bad that assisted by others in the cave party we can get 'em out before rescue is bothered (feed 'em and beat 'em works, minor injury that is workable but just slows the group down, maybe we took a wrong turn, a car broke down before we got back to cell signal, or we found a lead and lost track of time...etc) or it is SOOOO bad that another few hours for a later callout isn't going to matter in the scheme of things. After all, if something that serious does happen, someone is running out to call for rescue which will probably get out before the callout time anyway.
I'm on cave rescue here, and so are many I cave with. I know what response times are and agencies that have to be dealt with (we cannot self-dispatch, we must be requested by the AHJ), we are all volunteers spread out over a huge region...we are good, but it takes time. Heck many caves you have to drive 30min-1hr to, and then have a long hike before the entrance. I'm sure anyone in cave rescue realizes just how much time it takes...Golden Day not the Golden Hour! When we teach our intro to cave rescue course we say "assume for every hour into the cave a good able bodied caver is, it will be 10 hours for rescue from time of injury". Perhaps a bit long it sounds, but considering from injury, someone has to get out or callouttime passed, hike back to car, get back to cell signal, call 911, AHJ shows up, then Cave Rescue is called in, we mobilize, arrive on location, get gear hauled up mountains to the site, get patient stabilized and packaged, get 'em moving out....takes more time than one would think.
Of course, the 10 hrs for rescue for every hour in is true for *rescue* cases....there are plenty of lost people, and as I believe JV coined.... the "Feed 'em and beat 'em" phrase. I heard a story about Surprise Pit (our deepest in Alabama, 400+ ft, single pitch it's all completely freehang) some dudes did it, got to the bottom, decided they were too tired to climb out...JV was property manager at the time, got there first before anyone else showed up, went down, gave them food and water, and told them no one was hauling their ass out. If they wanted out, they had to climb. And guess what? All of a sudden they could all magically climb out! Hence...feed 'em and beat 'em! there are a lot cases like that where people just get tired biting off more than they can chew. Those sorts of rescues don't typically take so long, but there is no real injury.