Not necessarily, but it does dox any unused portion of that UTXO to the receiving country who could then track it's use into the future.

For example, UK sends 15 Bitcoin to NATO. The 15 Bitcoin come from a 35 Bitcoin UTXO. UK receives 20 Bitcoin back in change. NATO can now watch that 20 Bitcoin and gather Intel on how UK uses it.

This is what Whirlpool is designed to prevent. Without it, I don't see nation-states trading in Bitcoin with each other. The state may not care about your privacy, but it will protect its own.

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Yea correct it would dox the balance of the UTXO to the receiver but not to the rest of the world. Not sure that constitutes a national security threat since the two parties are willingly doing business.

UK is a major part of NATO. This does not mean it's ok with NATO having any more knowledge about it's finances than absolutely necessary. The state protects its privacy even from its allies.

Maybe they just use it as a store value and transact in some other means

Or the receiver will only accept payment in bitcoin so the sender might not have a choice if they want to transact