Government holding competitions for design, build, and maintenance separately was done for missiles, and it did not work well. Government has also designed at least one missile (Sidewinder by the Navy at White Sands), and the missile turned out well, although that was an example of a relatively simple device, designed for low-cost.
I think government focusing on specifying interfaces for modular components (in hardware and software) might be a good paradigm, though it probably has drawbacks which I haven't considered.
What I’m thinking is more like the Gov being able to furnish key designs to organizations that can plausibly iterate on them. So orgs don’t have to make massive investments to catch up to and integrate SotA phased array radars, flight controls, etc. Specific systems would still have single integrators.
There are probably a bunch of problems with this, but it’s certainly better than a specific organization vendor locking the Gov down a multi decade rabbit hole where key capabilities are proprietary designs and the vendor gets to dictate the direction/terms because it would take anyone else 5-10 years to catch up.