Tang isn't a NASA invention, it was invented by Kraft. It tastes terrible and no one bought it until NASA used it[0].
But lets run with that. If NASA had invented they wouldn't manufacture and give it away, they would give away the recipe and entrepreneuring businesses could make it to sell if they wanted.
This is exactly what happened with Memory Foam. A NASA contractor invented it as part of the contract so they couldn't keep it secret[1] and it worked its way into a ton of products.
I think you are correct that SLS is not ideal. But I don't think that is really applicable, their inefficiency as business is perhaps understandable because they are not a business. They take their direction from Congress and congress told them to make a ship out of parts they had laying around and that was the SLS.
If we wanted to look at their other missions, they have landed several things on mars and orbited distant planets. Feats no private enterprise has done (yet). All the research from that is available amateur astronomers routinely use to discover new things, like exoplanets in old data.
Designs for things they made like their rocket motors is made available, and that is how Space-X started, by looking at NASA plans for their rockets and picking and choosing the parts they thought most practical.
[0]: https://en.wikipedia.org/wiki/Tang_(drink)
[1]: https://en.wikipedia.org/wiki/Memory_foam