Arguing about somebody leaving their DC to cry for 15 seconds is a bit of a straw man anyway, I don't think there's any child in the world who has never had to cry for a few seconds! It's not usually physically possible to get to them in time to avoid that, and I don't think anybody is sitting there with a stopwatch counting 15 seconds until they comfort their child.
The main reason I won't do most "sleep training" methods is that I don't believe children need training to sleep - they sleep just fine if they are tired, relaxed, comfortable, and feel safe. Some are able to do that by themselves and some need the reassurance/presence of a parent to get that safety. It's likely to be an evolutionary thing.
But obviously sleep training isn't actually supposed to be about training them to sleep but about training them not to bother you. I don't really want to train my children not to bother me, not in this context.
I think some people believe sleep training teaches children to soothe themselves, but I don't believe this because I don't see how it could possibly work like that. You don't teach them to read by handing them Harry Potter at age 4, you don't teach them to swim by throwing them in the deep end with no arm bands. You start with things like picture books and the alphabet, and splashing in the shallow end. Sleep training is putting a very young child in a situation where they need to use skills they don't have yet with no opportunity to develop them or guidance on how they can do that. I feel it's important to cultivate the feeling of relaxation and safety around bedtime and then slowly wean the different parts away when I feel they are ready. Or just wait until they stop needing them by themselves, which they do.
But also, I have children who when left (because for example I can't get to them straight away or I don't realise they are crying until it has been a while) don't settle down but ramp up and get more upset/agitated. I think from reading some threads on MN that some children/babies don't do this, they complain for a little bit and then go to sleep. So sleep training probably works very well for those babies, and it's definitely not cruel in that instance.