In order for Bitcoin to be widely used for payments, it is necessary to stabilize price fluctuations.
Question,
Bitcoin and other currencies A and Prepare B.
A and B are equivalent exchangeable and can also be equivalently exchanged for Bitcoin.
Is it possible to stabilize prices through market mechanisms due to this?
No, if you want to do something like you proposed, you would actually have to back it with something much bigger than Bitcoin itself and with very low volatility, and you would destroy one of its main features. Anchoring Bitcoin into something that is centralized itself would add an element of centralization to a system that is made to be decentralized and exactly for that reason widely accepted.
Bitcoin's volatility is easily explained. Yes there could also be manipulation at work and that is most likely happening, but for the most part Bitcoin is based on collective trust and expectation. Since Bitcoin doesn't provide dividends like a classic stock, there is also no metric like a P/E ratio or any of those others numbers used to price a stock and make investment decisions accordingly. There is a big number of people who are not doing a lot of research but want to be involved anyway. Those are the people who also are most affected by either FOMO or FUD. They buy when everything seems amazing and they sell on bad news irrespective of the actual impact of those news. High trader sensitivity also leads to high volatility.
But volatility is also attractive to people in general. If it wasn't for Bitcoin's volatility, the global community would probably not be as big as it is. There is an upside and a downside to that.
It would be more important to decrease friction and increase velocity, making Bitcoin a useable currency for everyday transactions in every situation at every time in any place. The Lightning Network would be such a solution, but there is still a lot of work to be done before we'll see higher adoption rates.