I’d say the Skyhawk with a C bearing performs a “normal” bind as well as any yo-yo with that combination however for offstring binds that involve whipping the string into the gap you’re going to get more consistent results with the smaller bearing/gap. I can’t do that kind of bind, so I play with the C bearing because it’s what I’m used to.
The skyhawk with a C bearing handles snazzy binds really well. If you are having trouble with them, it’s practice you need, not a smaller gap. You are definitely right that a smaller gap leads to more consistent binds, but you have to be careful not to become dependent upon thin gaps to bind for you. I got the technique down myself by playing with a Fiesta XX with extremely worn pads. When I finally replaced the pads it felt like cheating.