Earlier quoted context omitted.
Let's say there are three BTC addresses in the world, #1 to #3. Let's say address #1 has 1 BTC that you're interested in. On Monday, all three addresses send all their BTC to address #4. The next day, address #4 sends the coins back to addresses #5 through #7. Which address out of #5, #6 or #7 has the original BTC you were interested in?
So - and thank you for bearing with me on this - individual BTC don't have a unique identifier that allow one to trace its transaction history? I must admit, I always assumed that they were uniquely identifiable.
A (non-coinbase) transaction is valid if its inputs equal its outputs, and if its inputs come from the outputs of other transactions, which in turn are valid if their inputs come from other transactions, all the way to one or more coinbase transactions. This is sufficient to demonstrate that the transaction is valid - ie it's using coins that exist instead of creating them from thin air. That is all that the protocol cares about.