I think your thinking in wrong direction, if more and more businesses accept bitcoins and create a natural demand for coins then we may need to mine more to meet the demand right? Also as of now lot of coins are with traders hand hence they will trade every day to make some profit with those coins, it makes it more unstable. When more businesses and normal people holds these coins then it will appreciate and it will more more stable price.
(My
emphasis)
Are you sure? Because I'd be willing to bet that there a lot more Forex traders trading non-BTC USD currency pairs than are trading BTC/USD. If I had to guess I'd say USD/EUR, GBP/USD, GBP/EUR and USD/JPY dwarf most other currency pairs. I seriously doubt BTC/USD is even in the top 50 currency pairs at this stage (I'd be
very happy to be proven wrong). In general people assume that the more actively traded a currency pair (or stock, commodity, etc), then the more stable it'll be.
I agree that mining follows price, however.
Because the other currency markets are very bigger than bitcoin market size hence by daily trading other currencies demand and supply will not change so faster compared to very tiny bitcoin market.