Good Idea / Bad Idea / Been Done - Mining reduces coin total

[mitchellmint]

This not something I am going to do to Trust but as an incomplete idea, and everyone knows how I like to make random coin maxes based on popularity but...

What if,

A coin could somehow use mining to increase scarcity through coding the total coin count to reduce by each block count.  Essentially the reward would go to an un-usable address intending the reward to be destroyed immediately.  This would force a miner to participate as a stakeholder, creating a larger risk/reward.  New money would be attracted to the scarcity. 

Good Idea / Bad Idea / Been Done?