hate to break it to you but NASA largely operates via private companies. Before SpaceX NASA was buying most of its launches from ULA which was just a defense contractor monopoly on the launch industry. During the Shuttle era, most of its parts were made by private companies, and usually the sourcing decisions were political (congressperson x needs a gasket made in their district) rather than like, trying to efficiently build a launch vehicle using public money.

For example, the Space Shuttle Main Engines were designed and manufactured by Rocketdyne. NASA refurbished them between flights, but for SLS (the next launch vehicle) they're being expended, meaning more money for Aerojet Rocketdyne.

Shuttle SRBs were made by a variety of companies, including Thiokol/ATK and Pratt & Whitney