Present company excepted
You can grow Brazil nuts, sell bonbons, fix brake pads and not qualify as a company or feature on an index. The world of small business does deal with promissory notes but they are the ones taking the risk by declaring that they will pay back the loan within a certain time. Nothing to trouble the markets.
Just as there are private companies whose progress isn't tracked so there is a world of folk warily wandering into degrees of commerce, often without a degree in commerce. They have stalls at the market or share some space or they work in their garage.
For all these folks, as well as the PAYE workers, there is not the capacity or the infrastructure to form a company and float it. This doesn't stop them trading. Nor does it make it of much interest to them whether a company has a president or not.
How many sole traders are there? Who are the most successful owner-operators? Perhaps this is an area of curiosity since it does help keep a competitive edge, emulating others.