I think you're losing out. The types of middle/upper management that look to startups from the enterprise have seen how to operate their part of the business at scale, even if it did mean a lot of meetings and red tape, and they are usually looking to work in a startup environment for the challenge and the ability to "make a change."
They might not be a good fit at the very beginning of the business, but they're probably essential post-funding.
They might not be a good fit at the very beginning of the business, but they're probably essential post-funding.