Per capita Norway exported ~20x as much oil as the US in 2007.

  Norway        554.24 bbl/day per 1,000 people  
  United States  28.08 bbl/day per 1,000 people

https://www.nationmaster.com/country-info/stats/Energy/Oil/P...

If they did export more, how much of the money would go directly to the US government?

The main advantage of Norway seems to be that they didn't give away their resources for pittances to private companies, but exploit them directly.

Related: https://en.wikipedia.org/wiki/Government_Pension_Fund_of_Nor...

You cannot compare tiny Norway to the whole of the US. You have to compare to individual states in the US. Many American states have more oil than Norway and has produced oil for much longer and at much lower cost.

Drilling a 4km deep oil well out in the north sea in rough weather is very different from drilling 20 meters on land in Texas.

If you look at various American oil states. They have managed their oil wealth far more poorly than Norway. No sovereign wealth fund. Public system often underfunded and in poor condition. Look at Oklahoma e.g.

Oil is not Oil.

There are as many "blends" of crude as there are oil fields (about 160 blends according to wikipedia https://en.wikipedia.org/wiki/List_of_crude_oil_products). Some are "thicker" than others and that results in different products you can get from the crude you refine. Also, each crude requires a different setting in your refinery, and it is very costly and lengthy to change that setup.

Refineries in the US are for the most part set to heavy crude.

Guess what kind of crude the US get's from fracking?

. . .

It's not heavy crude.