Intuitive is a term that has become way overused in the industry. When most people use the term intuitive, they actually mean that it has good learnability (the hamburger menu you mentioned being a good example).

Enterprise products should help represent the domain as experts in that domain think about their world. Since your Head of Product might not understand the domain (let alone be an expert), it is likely that they won’t understand the designed system. Getting feedback from your users that they love the product would go a long way (and may be the only way) towards overcoming this hurdle.