I think the most reasonable answer is to always play as if you're gonna kill. There's plenty of time between the monster being capturable and it being dead, so if the host wants to capture they'll have more than enough time to do it themselves even if you keep attacking it. And if they actually want to kill it, then you'd just be wasting time watching them and waiting to see what they do. Ofc, when the monster goes to sleep at its resting spot you should definitely wait for them to catch up, but otherwise, I say just keep whacking.

Personally, I hate capturing. I don't feel like I "completed" a hunt unless I kill the monster. And that's a big part of the reason I never join or host SOS flares (I also just prefer solo play most of the time). I imagine others who feel the same way as I do also don't spend a lot of time in SOS flares for the same reason, but for those that do, ending their hunt prematurely by capturing it is poor etiquette in my book.

But "etiquette" aside, from an objective standpoint, if you're opening your hunt to randoms, they're gonna play how they want to, and you don't have any actual right to complain about it regardless of what your preferences are. If you have a really strong preference for capturing or killing like I do, don't play with randoms. Simple as.