Earlier quoted context omitted.
Here's a real-world example: I sign and give you a transaction that, if you relay within the next 1000 blocks, will give you some BTC. You can choose relay it, to let it expire, or to resell it to someone else by signing another transaction that consumes my transaction's UTXO to you and grants up to the same amount to your buyer.
Does that actually happen, anywhere? How would you record the "sale" of the transaction if not on the blockchain? (If the answer is some other currency/financial system, consider what that implies for the overall utility of btc)
This is the basic principal of operation for a Lightning payment channel.