On the contrary, there are several companies who focus on making third party 5E content. Kobold Press and Goodman Games are prime examples (Into the Borderlands is the best-selling product in Goodman Games history).I think the idea that an independent publishing house could survive or even thrive off of becoming a third party publisher for another company's game is not necessarily a valid assumption to make. Fifth Edition makes Wizard of the Coast a lot of money. However, unless Matt Mercer or Matthew Colville are attached it has not proven to make anyone else a lot of money. Being #2 in the market, even if it remains a distant #2 provides Paizo with a good chunk of revenue.
Would they really be selling more books or get more prominent shelving space if they were selling source books and adventures for Fifth Edition?
Would they have to plan their release cycle around Fifth Edition? Paizo is already planning well into 2021.
If they start selling really well what does Wizards do to respond? What happens if there is an edition change?
I think the only way this would ever work is some sort of exclusive deal to make D&D branded products and given their history Paizo is loathe to attach themselves to anyone else's ship. They had to scramble and drastically change their business model because of decisions made by Wizards of the Coast before. Being independent to formulate business plans and steer their own ship might be worth it even if revenue is not as strong as it could be (I do not think that is the case anyway).