Doesn't intuition to resolve a domain specific problem require domain specific knowledge?
I've done operational improvement work across supply chain/inventory management, marketing, digital analytics, ecommerce, healthcare revenue cycle management, and call center operations. In almost every case I started with little if any direct domain knowledge. The intuition that was valuable for my work was around systems-oriented thinking applied to business processes and being able to quickly suss out weak or suspiciously opaque areas of the system. The necessary domain knowledge to do so was always picked up from domain experts as I went along.
In fact, taking a naive approach on domain knowledge has always worked in my favor to uncover invalid assumptions that those with domain knowledge just accepted without question.
That said, you're spot on that the core of what I do is data consulting, although most of it falls under a domain-specific name and has been W2, internal consulting roles. I'm actually in the process of switching my full time role to a less demanding one so I can focus on ramping up my actual consulting business.