jons - The best way to look at cost optimization, in my opinion anyways, is to think about it from the design/architecture and beyond. When you start with cost in mind, you will tend to be more efficient along the way. So, that being said, if you are new to Azure, it can help you learn to get that mindset, but if you are highly experienced, well, we all know things change FAST in the cloud, regardless of the vendor, so there tends to be some learning there as well.
As far as who is needed for these engagements, they tend to involve enterprise administrator and upper management levels, however thats not necessary to actually have the assessment performed (mostly). But, you come out of the engagement with some knowledge you may not have had before, and tooling to help you better control costs.
I have another post coming out tomorrow about the Well-Architected Cost Optimization Implementation, which is a second round for this assessment, so to speak, to actually perform cleanup and provide more knowledge.