If that really were the case, then I absolutely can't see any reason to increase the money supply.
Let's say the entire population consists of:
Alice who has $10
Bob who has $10
Ben B. who has $5
Ben decides to double the money supply, distributing equally as you have suggested.
Alice now has $20
Bob now has $20
Ben B. now has $10
They all have exactly the same purchasing power as before, so the whole exercise was pointless.
The only reason I can see for Ben B. to increase the money supply is to increase his (or his friends') percentage of the total purchasing power (Which is basically a tax on Alice and Bob).
Why else would he do it?
This is one thing bitcoin can do by adding a fixed multiplier to each block such that at the end of the day the output value of each block 24 hours old is doubled. The client would do this when calculating the value of a block that is buried n blocks deep in the chain.
You have 10 bitcoin today -> tomorrow you can spend 20 bitcoin.
A recipe for hyperinflation for sure :-)