Reward for those running the full client possible?

[Stevets]

Has anybody ever considered some clever way for the protocol to reward those running the full client? Maybe this what "minting" is all about in Peercoin. I don't think it is, because as I understand it, minting just pays interest on coins you already have. What I mean is some kind of consolation prize for those of us who support the network for free.

Maybe the reward grows with the blockchain size. Then the blockchain size is no longer an ugly wart but a source of BTCBTC

I don't know where the coins would come from. Maybe a percentage of new coins mined, a percentage of transaction fees, an additional transaction fee, donations, something else?

This has probably already been discussed but I didn't see it.