Personally we're not the leashing type. With 3 kiddos we don't leash. However we do use the buggy for certain situations. We also use a carrier. If we can't pay full (or at least 70%) attention to the kiddos, then they need to be contained.
We lost our (then) 2 year old for 45 min a coupe trips ago. I thought DH was watching the girls, he thought I was, we both looked at the menu at the same time and she was gone (from Pop). We were eating beast, then heading to the airport. She wanted to go back to see the Mouse. She walked off beside another family, and right onto the ME bus.
It was 2 seconds worth of inattention, and that's all it takes. It doesn't matter how 'attached' or how attentive we are the rest of the time, those 2 seconds are what mattered. If we'd had a little pack on her with a tether, we wouldn't have ruses to the pool terrified, we wouldn't have dashed to the streets wondering if a bus would even see a toddler. We wouldn't have thought about the hundreds of cars within seconds of the resort doors.
In the parks I wouldn't be as concerned, but in the resort? there's really no safety to prevent a child from being snatched. There's no safety to prevent a child from falling into the pool, there's no safety to prevent a child from falling in a lagoon and being eaten by an alligator!
I don't leash now, I'd said once before I never would. I've looked down on those who do leash, and will probably still get annoyed when I see a parent dragging their leashed child along rather than paying attention to said child. However I will not say leashes are inherently bad. And on our next trip (116 days away) I will probably leash our soon to be 19 mos old.
We wills till pay attention to our children. We will still use the carrier, we will still use the buggy, but they will each be used at different times and for different reasons. Each item will allow our children to feel secure while also allowing them to feel independent. Win-win IMO.