This is not quite true. There is a unique identifer even from when the bitcoin is minted in the Coinbase block.
When a block is found, say 50 BTC as an example, then each satoshi doesn't have a unique identifier however once those 50 BTC are spent then they have unspent outputs which have a hash. So if someone sends that 50 BTC to 1 person, there is 1 UTXO, but if its sent to 50 BTC then there are 50 different unspent outputs.
And those get all spents and the trial goes on and on and eventually different blocks are combined with one another and its difficult to trace them but its still there.
Learn me a Bitcoin has its explanation on "How bitcoins are used in transactions and how UTXOs are created"When a block is found, say 50 BTC as an example, then each satoshi doesn't have a unique identifier however once those 50 BTC are spent then they have unspent outputs which have a hash. So if someone sends that 50 BTC to 1 person, there is 1 UTXO, but if its sent to 50 BTC then there are 50 different unspent outputs.
And those get all spents and the trial goes on and on and eventually different blocks are combined with one another and its difficult to trace them but its still there.
https://learnmeabitcoin.com/beginners/guide/outputs/
Practically, spending all bitcoins you have is rarely practice especially if it is big fund. In addition, it is not a recommended practice to protect your privacy.
General guidelines for sending BTC transactions with privacy improvement.
One of advises is
Quote
Don't send round numbers
Don't send round amounts. Instead of sending 0.1 BTC, send 0.10125
Don't send round amounts. Instead of sending 0.1 BTC, send 0.10125