The C- Suite is a 20th century idea. And Product is a nineteenth century one. Both should not be relevant to a modern business and both CEO and Product Manager thinking should be consigned to history.
The key change was made by Napoleon. He structured his Grand Armee so each unit could operate independently, acting as flank, vanguard or rearguard at will and making decisions on the fly, without reference to the overall leader. It was phenomenally successful, defeating armies many times his force's size and when he was eventually defeated by the combined might of the aristocracies of Europe they adopted his methodology.
It moved to the next stage after 7 million deaths in WW1 showed the folly of centralised control with small teams of experts banded together in units with each member deferring to the expertise of the expert in that part, yet working together collectively. Today these small, flexible units which make fast decisions are essential to combat guerrilla tactics by terrorists using similar organisational systems.
Industry, however, went happily on with the egotistical hierarchical model and it was given added impetus with the first generation of software which created deep silos based around each group's version of the truth. The effect was to create large ineffective organisations - the exact opposite of the intent to share information to be more agile.
In modern companies a new method is taking over - these same small units. Here roles are flexible - if one person has a flair for organisation, another for vision and a third for communication, they can split out responsibilities to suit. The leader is just as likely to be a technical person as a people manager and roles may even switch according to task, project or outcome.
Product focus is a hangover from the industrial age, where automation in factories created a physical product in quantity and undifferentiated across all markets. It was naively believed that the best product would always win and a product manager was the champion of the process to win this feature race. Often the race was to the bottom as with long production runs every cent saved put millions on the bottom line of the company.
Now product is only one of the 4Ps of People, Process, Profit and Product which together make up the creation of a "product" and product-market fit allies it to the markets it serves. In this environment a product manager is a dangerous silo - innovations in other areas are just as likely to give the company the edge.
Consign CEO to the bin. And Product Manager.
Then think again around teams - fluid to suit the skills involved and which start with the market, working back together to what you need to offer. And keep it fluid - people change, whether customers or employees.