A Bitcoin-only economy would probably look like the global economy back in the days of the Gold Standard. Inflation would be very low, but the economic growth would also be really low. The problem is that such Bitcoin-only economy cannot happen in real life, because the BTC blockchain can't handle billions of transactions every day. Maybe there would be offchain/sidechain solutions, that would solve that problem, but they would most likely be centralized and charge transaction fees on top of the blockchain transaction fees.
Bitcoin is volatile because of two main factors:
1.Fiat currencies keep losing value.
2.Bitcoin mass adoption is an ongoing process and the majority of the global population still don't want to use Bitcoin.