Essentially, I want to know if the copywriter can or should help us craft our 'why'.
This sort of depends on how established or large your company is, and what you want as your messaging. A good copywriter can certainly help you find *a* "why", though it might not be *the* "why" you actually began with. For example, if a web hosting company got started because two college roommates needed money to pay for tuition, that's a very important story, but it doesn't really sell as a "why". A good copywriter would come in and put some spin on it like "Steve and Dave knew starting their own business together would be hard, so they wanted to create something that would make entrepreneurship easier for others. At ACME web hosting, we make this our mission every day". It's now a great story, and sounds like a caring company... and it can even be true... but it's not actually the real reason the company started.
A good strategy is to cast your mind back to the feelings you had when you started your company. Just write them down as one word emotions, and then on a separate page, write down the emotions you feel about your company *now*. A good copywriter should be able to find a story in there, and help you position your company in the best possible light, even if through rose-tinted lenses.