Lufthansa tried a direct JFK/DUS 737 with 50 seats all business class, single price 10 years ago. Didn't work.
The biggest profitable customer is the "company travel policy." Mine requires a restricted fare coach ticket, cheapest within 2 hours of when I need to leave. Which is why a full-fare coach ticket is frequently almost the same price as a first class seat. An all-premium cabin would be very difficult to market to corporate travel buyers.
From the perspective of a couple large companies I have worked for over the past two decades:
Boeing: Domestic travel below exec level emplyees, cheapest fair available on the route. Exceptions available for flight times that accomodate schedule required. Cheapest is defined as within ~$200 of the lowest available fare before the system flags it as out of policy.
International is First class for any domestic portion and Business class on International Segments.
GE: Domestic and International travel below exec level emplyees, cheapest fair available on the route. Exceptions available for flight times that accomodate schedule required. Cheapest is defined as within ~$200 of the lowest available fare before the system flags it as out of policy. There used to be a 10 hour rule for First class, but that was recently removed.
Over the years I have kept most of my travel to AA to retain my Plat / Exec Plat status to keep the perks. A few trips I have had to move for pricing (Saudi Arabia was $12K on mixed carrier vs $15K on all One World for example). I also wouldn't fly Southwest for business and managed to avoid the "Out of Policy" police.