Despite widespread adoption of Bitcoin by mainstream businesses, companies, and governments alike, prices relative to Fiat haven't stabilized yet.
This is the issue, Bitcoin's price hasn't stabilized because it hasn't been mass adopted yet. There's a general acceptance by most people that crypto's serve some sort of role, but when you ask people if they're involved in crypto for day-to-day use, they'll tell you no. People are using Bitcoin as an investment oppose to an actual currency, if they use crypto currency at all, so we're not at the point of mass adoption. I consider mass adoption to be the point when Bitcoin acts as the world's reserve currency, toppling USD. Perhaps a big goal, but not unrealistic if you've seen how other currencies are operating at the moment. Once true mass adoption occurs, then the price stabilizes.