What about a protocol that used the figures in percentage (in scientific notation, sure) relatively the totality of bitcoins instead of a number of bitcoins that is completly arbitarily.
The protocol only knows satoshis (1 satoshi = 0.00000001 BTC). So the client display code is what knows the concept of a bitcoin. So you are simply describing a change to the display portion of client code.
You code create a fork of the Bitcoin-qt client to do this.
I can't think of a single person who would want it (except maybe some mathematicians who might like the novel look) but there isn't any technical reason this couldn't be done today.