What problem are you trying to solve other than "I don't mine so I don't like it that other people get subsidized coins"? The primary purpose of mining is to secure the network. Any system that discourages mining is working against the basic interests of the network.
I'm not trying to come up with a network that discourages mining, that should be rewarded as much as possible. I was just thinking how I could encourage some actual usage too.
It would be nice for people to be able to earn some coins, without expensive hardware, just by participating and some luck. There was a time Bitcoin had lots of faucets for that purpose, but that was just giving away free money to anyone who asked, causing lots of fraud. While my automated approach only gives it to the people that deserve it (those who make actual transactions and paying the fees for that). The end result is that the coins are more evenly distributed across the world population, and you can't possibly be against that?
There are many alt coins that have lottery functions (lucky coin) and other proof of stake coins that reward you for "participating". You should check them out. Also look into X11 algo which gets people back to CPU mining.
The ship has already sailed for Bitcoin and its fundamental nature /distribution mechanism isn't going to change so if it's Bitcoin you want to affect, you need to find another way to give out coins (cool contests, etc)