But the U.S. government does own quite a few companies (a number even have the word Corporation in the title), for one example the Tennessee Valley Authority. Among others are Commodity Credit Corporation (CCC), Fanny Mae, Freddie Mac, FDIC, Amtrack, Corporation for Public Broadcasting, Corporation For Community Service (AmeriCorps), Federal Agricultural Mortgage Corporation, and the USPS, among many others of course many of these are controversial.*
Long ago I worked for the U.S Geological Survey and they had a patchwork of contracts that at one time were done by their employees. These included such things as the library, a shuttle going from the headquarters in Reston, VA, to the Interior Dept in D.C., a photographic operation, mail delivery in the 7 story headquarters building.
The mail contract was won by an organization of mentally deficient people. I thought the mail delivery that had been awful was going to get even worse. When these guys got the routes down, you better get out of the way in the halls because the mail was going through. These mail people tended to be physically disfigured as well. Once I went into the mailroom where a bunch of them were and it looked like a Far Side cartoon.** I got on an elevator once where a young sturdy large young man was already. As the door shut he said to me, "Why do you hate me?" He had arms like tree trunks and I was a little scared, well, a lot scared. I said, "I do not hate you." and got off at the next floor.
* (https://en.wikipedia.org/wiki/State-owned_enterprises_of_the_United_States) of course many of these are controversial
** https://www.google.com/search?rlz=1C1PRFC_enUS655US656&q=far+side+cartoons&tbm=isch&source=univ&sa=X&ved=2ahUKEwimqZH_4PjiAhVP2FkKHd4jBkoQ7Al6BAgDECU&biw=1232&bih=796#imgrc=UYK4vucZNmQ5QM: