Hiking I usually carry some sort of bag, often a butt pack or gas mask bag rigged with a shoulder strap, or backpack and the canteen/cup rides inside if there is room or I clip the canteen cover to the side.

I've, over the years, moved away from the Bat Belt, everything on the belt, and use of military load bearing equipment where everything is hooked onto a harness or vest.

The belt or harness systems are intended to keep the gear with a soldier or police officer in danger. It is a concern but carrying a pack or bag I've never been separated from it. I have sometimes attached a lanyard or cord to a pack that is tied off at my waist if I ford a river or think there is some risk me and my gear might part ways. A few of my bags and packs have a lanyard sewn in with a sturdy clip at the end that makes attachment quick and easy.

I do use lanyards. For example in my first-aid kit the flashlight, SAK, and EMT shears are all on lanyards clipped to the bag.