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.