Agreed — while we’re at it, let’s break Boeing up into multiple firms. It has been “too big to fail” for too long.
Break them up and it's easier for both the market and the government to punish bad behavior.
They all have the rights to the existing designs, and can create derivatives, but they don't automatically get the rights to the others' derivatives, so they have the incentive to specialize or develop new designs to find a niche, for the same reason the Boeing 737 isn't an exact clone of the Airbus A320 or vice versa.
If there were more competitors, they'd lobby to change how the regulations work so they didn't effectively destroy the market for new aircraft types.