Not all Pokemon have access to moves like sharpen, amnesia, rock polish, nasty plot, or swords dance. Using choice items is one way to compensate for that. One example includes Mamoswine (monotype), which doesn't have any means to boost its attack or speed, so it usually uses band or scarf.
Most of the time, the Pokemon that use band / scarf / specs / assault vest are either too frail or need the instant power. One example includes stuff like Hoopa-Unbound. Sure, you could run a nasty plot set. But the fact that nasty plot takes one turn to set up and the fact that Hoopa-Unbound is either too slow or is weak to any physical attack makes this set difficult to use. It's much easier using band / specs to get that attack boost.
Scarf is an interesting case because it reaches speed tiers it can't normally reach. You usually use it to revenge kill another Pokemon - if one of your Pokemon faints, you might swap in a scarfer because it outspeeds your opponent's current Pokemon. If it had Rock Polish, Agility, or some other speed boosting move, you don't get the same advantage here.
I'm not gonna talk too much about assault vest, since I don't see it often, but yea most of the time Pokemon won't have access to Amnesia.
tl;dr: Pokemon will either not have access to boosting moves, or boosting moves take too long to set up for some of the frail Pokemon that do have access to it.
This isn't to say that boosting moves aren't completely useless - there have been effective sets with swords dance or rock polish Landorus-Therian, even though scarf is also a viable option.
edit: just noticed sumwun's post - choice band and choice specs should have a multiplier of 1.5x
