The classical economists didn't really assume that capitalists played fairly. They were much more Hobbsian. For Adam Smith there is the famous "invisible hand" which has a negative feedback effect upon what would otherwise be a dirty fight to the death between rival firms. The invisible hand means that there is nobody setting the rules, but that needs nevertheless somehow get met via a market equilibrium.
Marx also didn't assume that capitalists played fairly, either with workers or between themselves.
To extract the maximum amount of value capitalism always has an atomizing effect, breaking up feudal clans, artisan guilds and proto-union combinations. The proposed squad level organization will be less efficient at value extraction, so trying to compete on the same ground will always be a losing proposition.
You can think of it as the extra value created by operating as a squad sized team is value which would otherwise be appropriated in a more conventional employer-employee relation.