i note the reactors you describe are all government owned, yes?)
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First, the facilities I named were not reactors; they were reprocessing facilities.
The French facilities at LaHague are government-owned because in France the government owns the whole electric network, the nuclear power plants that produce the energy, the grid, the reprocessing plants that deal with the waste - so there's nothing special about the reprocessing facility being government-owned.
The US facility I mention is government owned; but why is that?
I wish the anti-nukes would be consistent, or at least study the history to know what decisions their anti-nuke predecessors made. Back in the '70s, the nuclear industry was prepared to take on the task of cleaning up the "backend" of the nuclear fuel cycle. The industry was building reprocessing facilities. West Valley Nuclear Fuel Services undertook building a reprocessing facility in West Valley, New York. Another facility was undertaken for Barnwell, South Carolina.
However, the anti-nukes at the time said, "We don't trust you evil corporations to do the job of nuclear waste disposal properly. You won't do it right, and you'll cut corners. We don't trust you." So they got Congress to outlaw reprocessing by private industry. The policy would be that the Federal Government would do the job of waste disposal, but the industry would pay for it by paying a special tax to the Nuclear Waste Fund. That's the situation we have today. Congress made the industry scrap their plans for doing it themselves.
Now the anti-nukes ask, "Why isn't the industry stepping up to the plate to deal with their waste. Why does it always fall to the Government to take care of the waste?"
It's that way because a previous generation of anti-nukes wanted it that way.
PamW