They are not saying governments should have control of this power. They are just saying no private entities should have control.
From the article:
> In a joint statement, the two governments affirmed that “no private entity can claim monetary power, which is inherent to the sovereignty of nations”
I parse that as: monetary power is inherent to the sovereignty of nations; thus, no private entity can claim it.
It's like saying: "No dog should be allowed to eat chocolate, which is toxic to animals."
It would be helpful to have the actual original statement, but I wasn't able to find it very quickly and gave up.
In everyday English, it would be obvious, but regulators and politicians are not bound by that.
"It's obvious" is rarely a good argument on this particular site. If it were obvious we wouldn't be talking about it.
I don't think it's being used in a legal sense in the statement quotes in this article. If it is, I'm not sure how "private entity" is defined in the EU, France, and Germany.
"Private entity" actually is clear in common English, but my experience is that governments tend to take words from common English and use them differently.
If you have specific legal experience with this term in a particular legal jurisdiction---and you very well might---it would be helpful to say so.
I doubt the use of the words "private entity" was specifically intended to exclude decentralized currencies. It probably actually means "anyone who is not us."