This is the reason why I don't agree that Bitcoin should be seen as "Digital Gold" as it lacks this quality, it's like every gold bar is stamped with previous ownership and you can't melt it.
Your analogy of a UTXO being a gold bar with a stamp is accurate, but contrary to what you might believe, a transaction "melts down" UTXO "bars" into new UTXO "bars" with new stamps. It works exactly like gold.