Cameron Herold says the COO's job depends on the CEO's style. If the CEO is the public face like Steve Jobs, the COO runs operations quietly. If the CEO stays behind the scenes, the COO becomes the spokesperson.
Chapters
Some CEOs are so outward facing they become integrally tied to the marketing of the brand as Steve Jobs did at Apple or Elon Musk at Tesla. The general public is almost as familiar with the CEO's name as with the product. In those cases the right COO is likely more inward facing and focused on the behind the scenes operations. There's no reason for them ever to become known to the public. In contrast other CEOs are inward facing. They're like the level five leaders Jim Collins describes in Good to Great humble, driven, focused. A combination that allows them to be inspirations for their colleagues rather than engaging with marketing and branding. They might specialize in engineering or finance and lack any desire to engage with the media. This type of CEO can build a highly recognized brand without their name becoming widely known. In such a situation a public facing COO would make sense to serve as the face of the company in the media and the spokesperson of the business world.