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
The amount of persistent storage is not as big of an issue as network bandwidth is. As a full node, you'll have to download every new block and every transaction as well as send them to your peers. Bigger blocks = more network bandwidth consumed. Make the blocks big enough (= several MBs) or block interval short enough and it could be terrabytes of network traffic per month.