You would need institutions to do this? What do we have besides global megacorps with the resources for this? Universities perhaps training models for their local catchment?
We'll probably see a few middle-tier countries like France or Japan training their own national LLMs that they can control. Even if it's expensive, this will eventually be just as critical to national sovereignty as having nuclear weapons. They don't want to be completely dependant on the USA or China.
I can see a pan European project like CERN or Airbus where sovereign nations with aligned values pool their resources, as being useful here