If Boeing has insufficient competition, they don't have to care because their customers have limited alternatives. If they don't have to care then they don't have to care if their subcontractors care. They also have limited fear of regulators because the US government will be wary about damaging the country's sole supplier in an important industry.
Break them up and it's easier for both the market and the government to punish bad behavior.
Make five of them that each have full rights to the existing company's designs and split their existing physical plant between them. Does one of the new companies have the only plant that makes a certain type of component? That's fine, customers can buy from them like they buy from the existing Boeing, but now the other sister companies have the incentive to build another plant to compete for that business, and the first company has the incentive to keep prices competitive to deter them from doing that. For five years they have to sell to each other for cost, giving them enough time to either negotiate with each other or build new facilities.
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.
You realize how type ratings work yeah? An airline wants to fly a common model. They wanted a 737. They would buy a worse plane for twice as much (see: 737 max) over a brand new clean sheet model that’s incompatible with their pilots.
Type ratings work that way because there are so few types of planes, and because the incumbents like it that way. "Oh no, I guess it's impossible for anyone else to produce a new aircraft model because nobody's qualified to fly it, now we'll just have to rest on our laurels forever."
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.
The FAA is susceptible to Boeing, the huge conglomerate and defense contractor, not any random airline that could go out of business without anybody really caring. But the status quo is good for Boeing because they don't have to pay to design new stuff, or at least they're ambivalent to it. Change that and see what happens.
Break them up and it's easier for both the market and the government to punish bad behavior.