I’d totally support that.
As far as I understand it up to now, the transactions that lead to rewards happen on another layer, but nevertheless it’s kind of frustrating to not see the details in the “official” wallet and to not be able to trace these transactions in the “official” explorer.cardano.org. Fees just vanish into the thin air out of which the rewards appear, when they are claimed by a withdrawal from Yoroi or some transaction using them on Daedalus.
Even PoolTool gives a warning: “Please note that due to how we calculate rewards you may see some minor differences between daedalus and pooltool.io.” (And we should not need a third party service to see such essential information, anyway.)
In order to verify that everything is handled correctly, the nodes have to know, where exactly fees are going and where exactly rewards are coming from, so it should be visible in a full node wallet like Daedalus and completely traceable in the main Cardano Explorer.
FWIW: I have summarised some of the missing, incomplete, intransparent information in the different block explorers, here: Comparison of Block Explorers