If every year your coin splits so now you have 2 coins then 4 etc no money was added. I can have 10^1000 in a database, but that's not new value.
https://github.com/ethereum/wiki/wiki/Proof-of-Stake-FAQ
Staking doesn't produce new coins. It pays dividends from transaction fees. I.e. actual economic activity.
Lets say I Buy '1,000' tokens including a 10 token payment for a transaction fee for 1$. Now A had 1,000 tokens and now has 1$, I have 990 tokens and another group get's 10 tokens. But, notice that other person(s) got tokens not money.
If I got to keep 1,000 tokens or someone else get's those 10 tokens nothing changes because nobody who has tokens got any money. The only way people with tokens get money is if they sell some number of tokens minus a fee to someone else. It does not matter of all 10 tokens go to a miner, or miners get 5 tokens an 5 go to 'investors' or what not.
It's still a (edit: negative sum game) and contracts don't change anything about this.