Yes, but it should be in the mempool when verified close to the time of mining, shouldn't it ?

Then it would have to be stored along with the blockchain (i.e., this doesn't help if the amount of persistent storage is an issue) and you'd need some mechanism to update nodes that don't have that data, plus you need to handle cases where, say, a new block overtakes a transaction referenced by it, but I think the "tip" of global activity should generally not need much extra work.

- Werner