The hypothetical scenario where the mempool size reaches 1TB, surpassing the entire Bitcoin blocksize to date, was used to illustrate potential challenges including free relay attacks. This stems from the logistical impossibility of mining all broadcast transactions under such conditions. The concept of one-shot replace-by-fee-rate as opposed to pure replace-by-fee-rate mechanisms was proposed as a solution. This method, while still ensuring a form of proof-of-UTXO ownership similar to existing transaction replacement mechanisms, introduces a nuanced approach to how this proof is verified and utilized. For further details, Peter Todd's insights can be explored through his website.