The effects on block data transfer of prioritizing "old-enough" transactions when building blocks

Had this thought:

Full nodes already re-assemble blocks based on transactions they already have (with protocols like CB, XThin or Graphene).

If miners were to prioritize including older transactions, then the efficiency of these protocols would increase.

It would also be a policy which is good for the users of the network because the longer your transaction has been around, the more likely it would be included in the next block, if miners were to adopt such a common approach.

It would have a cost to nodes in terms of tracking when a transaction has first been seen by them. This might become large if the mempool is big, but so far the mempool and block sizes are very small compared to the memory sizes of commodity computers.