Also the I part of ISS kept the world space research orbiting around NASA. For example Brazil make every single research that requires a station (including vehicles, modules and medical science) use the ISS.
Without the ISS Brazil could for example attempt its own station, or help China instead.
NASA is very powerful, but if everyone help China or Russia instead, it would be bad for USA strategically.
As a NASA employee, I find the phrase "NASA is very powerful" amussing in any context. That said, I think the far more likely outcome of the ISS being abandoned without a replacement would be that most countries would simply not invest at all in space-based research. The Russians just don't have the budget to build a station on their own, and I doubt the Chinese would welcome international collaboration.
I am not sure that many countries would want to get involved in the Chinese space program, which has always been secretive, and dominated by nationalist goals rather than scientific ones. It seems that the Russians would welcome other participants in their program, though it seems unlikely that Brazil would want to fund what appears to be a struggling and lackluster Russian program.
I am also not sure why a reduction in international collaborators for NASA would be strategically bad for the USA. I am a strong proponent of space exploration, but NASA is not an important part of US military strategy; NASA is mostly a luxury which allows the US to demonstrate its technological supremacy.
"Control" of space isn't a big deal as long as nations respect the no weapons treaty. Afaik it is possible for ground-based weapons to destroy satellites too. I guess a satellite that could find submarines or hidden nuke sites would be useful in peacetime, if you were planning a first strike.
Without the ISS Brazil could for example attempt its own station, or help China instead.
NASA is very powerful, but if everyone help China or Russia instead, it would be bad for USA strategically.