Similar difficulties exist in handling an old transaction that was created before a soft fork but was broadcast only after it, and became invalid under new rules.  The rules must have changed for a reason, so the transaction cannot simply be included in the blockchain as such.   For example, suppose that the change consisted in imposing a strict limit to the complexity of signatures, to prevent "costly transaction" attacks.  The miners cannot continue to accept old transactions according to old rules, because that would frustrate the goal of the fork. 
(Note that there is no way for a miner to determine when a transaction T1 was signed.  Even if it spends an UTXO in a transaction T2 that was confirmed only yesterday, it is possible that both T1 and T2 were signed a long time ago.)