The current airline which most closely resembles your idea is La Compagnie which flies between Paris and Newark in an all business configuration.

Their fares are substantially less than the competition in business and in many cases are competitive with coach ($1400 or $1500 roundtrip).

I do think that there is a market for business-lite products. The main issue is that it will be very difficult for a standalone startup like this (or like Maxjet, Silverjet, Eos etc) to be the one to successfully introduce this to the market as the competition has enormous advantages from vast route networks, flexible fleets etc etc.