It's only more profitable if you have surplus manufacturing capacity. If it was more profitable for companies to build their own designs the contract manufacturing industry would exist.So who else can build them? Well Fairey was the obvious choice, but firstly it was already committed to developing the Fulmar. At the end of 1938 the Admiralty tried to persuade Richard Fairey to build Spitfires for them. But he wasn’t interested in building someone else’s aircraft designs (still peacetime - more profit in building his own designs). So you need to find a manufacturer with spare production capacity even if Supermarine have the design capacity in late 1938, which is perhaps open to question given the other projects they had in progress at the time.
The cost of manufacturing equipment - furnaces, presses, machine tools, building space, etc is a huge expense. Having staff good at both design and manufacturing is something only handful of companies successfully achieved.
And if you start manufacturing for the competition, you won't retain your own design team. Then, if requirement for the product you are building dries up, you have nothing.
Richard Fairey (and Sidney Camm) were protecting both their design and manufacturing teams.
IMHO, FAA planes would have benefit from 2 (or 3) speed supercharger like the 2 stage P&W powered USN planes did (Neutral to 1k', low to 7.5k, and then high - effectively giving 3 speeds)