I think founder mode is related to the Theory of Constraints[0]. When a founder is already successfully growing a company, they have experienced pushing past many different constraints/bottlenecks of their company. Usually this includes some understanding of the constraints of their industry or they wouldn't have founded a company. Most manager mode advice will be irrelevant to the current company constraint, but can take resources away from solving that constraint. The founder can draw on the knowledge of past constraints and focus on what is important for the company.
For all his problems, my example of this would be Elon Musk and SpaceX. He learned about the space industry and identified the constraint keeping the space industry down. Every launch provider was trying to maximize the performance of their rockets. To maximize performance each rocket was basically a bespoke work of art, this made rockets expensive, which lead to high costs, which reduced the number of customers. Musk chose to make a rocket that did NOT maximize performance, instead focused on reducing the cost of each launch. The most expensive part of a rocket are the engines, so SpaceX focused on making Merlin engines at low cost. Rockets are expensive, why are they thrown away? To maximize performance. Since SpaceX had already abandoned maximizing performance at all costs, the opportunity to reuse rockets became clear. Use leftover fuel margin to attempt to land and reuse the rockets.
Once Musk believed SpaceX's reuse was going to work. He moved onto a new major constraint, customers. SpaceX did not and does not have enough customers for the launch volume they are able to support. They looked at the opportunities and decided that a large constellation of satellites providing fast internet access in LEO would be profitable if launches were now cheaper. So SpaceX created Starlink to take up launch volume.
[0] https://en.wikipedia.org/wiki/Theory_of_constraints