> We already have the right to station as many troops there as we want!

Only at Thule. The 2004 re-agreement rescinded the unrestricted establishment of bases:

https://www.state.gov/wp-content/uploads/2019/02/04-806-Denm...

It significantly emasculated the 1951 agreement:

https://avalon.law.yale.edu/20th_century/den001.asp#art2para...