The problem is that for a real currency you ideally want inflation to match the growth of the economy. Fixed inflation rates (including 0) are decidedly non-optimal.
There are arguments in favor of the fixed supply model. The usual economic one is this:
When you earn and stockpile currency units, what you are doing is producing more than you consume, so in real terms you are allowing others to temporarily consume more than they produce. This essentially means that you are investing the difference into society as a whole. Thus, it makes sense that if the economy grows by 2x, your currency units should grow 2x in value, as that's the way any other investment works.
When you earn and stockpile currency units, what you are doing is producing more than you consume, so in real terms you are allowing others to temporarily consume more than they produce. This essentially means that you are investing the difference into society as a whole. Thus, it makes sense that if the economy grows by 2x, your currency units should grow 2x in value, as that's the way any other investment works.