I agree with what you are saying. Don't get me wrong.
Lets just say SpaceX buys out NASA's interest in the ISS.
They go along with the 'order' of business for the time being.
Then, another private entity buys out the ESA's Interest in the ISS.
Then a series of private buyouts removes the government interests of the station completely.
(There is also the possibility that one entity could buy out all the government interests completely.
Similar to the S. R. Hadden scenario in the film Contact (1997). Individuals do have enough money to buyout the station.)
Now we have a bunch of different private entities 'owning' a conglomerated station.
They agree to use the station as a platform for constructing their own facilities in space.
They pool their knowledge and resources like a Type 1 civilization would.
The ISS becomes the centralized hub much like a United Nations but a United Business instead.
The concept may be too 'mature' for our current business world. Businesses still operate on the Mine, Mine, Mine pretense of profit over benefit. Perhaps this would change us from individual profit seekers to united species benefit seekers.
This frees up resources for government sponsored projects like manned missions to Mars, research missions to various moons and other space bodies. The ISS is still a vital part of that scientific expansion but instead of governments needing to maintain the station, they become paying customers. The widgets get fixed by the owners, not the customers.
I'm sure its all a lot more complicated. People have a knack for making simple ideas complicated.
What I see tho, is a stagnated space expansion if privatization does not gain a foundation in space quickly.
The "I" already greatly restricts the possibilities of the ISS. There are a lot more restrictions for a national interest than a private one. The first is accountable to en entire nation while the other is accountable to a smaller group of shareholders.
I'm sure, given this announcement, there are lawyers working on the legal aspects. Everything Trump does is inspected with high scrutiny. I'm sure there will be agreement and disagreement and a huge turmoil over it all.
Personally, I see privatization of the ISS as inevitable. I see it as a good thing in a type 1 civilization kind of way. I see it as a unity of the people of the planet Earth that will put new interest and money into space exploration. In a science fiction mindset, it opens many new possibilities for our future.
I don't have vested interest no matter the outcome. My taxes are not within my power to dictate. I will not lose anything by the ISS going private. I do, however, believe I stand to gain much in the sense of progressing towards the next step in space.