Not at all. It naturally stabilises the closer it gets to its ultimate market cap. The more it stabilises the more it will be used as a medium of exchange.

There is no evidence for this. When gold and gold-backed currency were used for trade, it fluctuated in value wildly and there were several depressions each decade. After centrally-issued fiat currency was introduced, it had a much more stable value, since it could be issued counter-cyclically.