As Bitcoin is a digital-specie currency, if it replaced all fiat currencies it would be the equivalent of reverting to a (digital) gold standard and can be answered in much the same way.
Firstly, a gold standard is deflationary. Explaining this again and again is tedious, so I'll summarise:
- People provide goods or services to others and receive IOUs for other goods and services, redeemable on the rest of the world; this is the essence of money.
- As more people interact and do so faster and faster, the money supply must expand to reflect the transaction volume; otherwise earlier unredeemed IOUs are worth more than new IOUs for the same goods and services.
- A currency with a fixed limit (be it Satoshis or Gold atoms) will either not expand (everything has been mined) or will expand slower than the rate required by the economy for its money supply1.
- Hence, either society cheats and detaches their promissory notes from an exact gold amount (fractional reserve banking and the like) and thus moves towards a fiat currency; or suffers the acute boom and bust cycles of purchasing power and liquidity depending on when hoarders hoard vs sell their stockpile. If you are that lucky. Strictly speaking, hoarders as rational actors would hoard forever and the entire economy would need to bootstrap from barter or a different currency.
Secondly, possession of a deflationary currency encourages hoarding if the society is forced to use only that currency.
A person with a large amount of deflationary currency will consider it an investment as its purchasing power will increase the longer they don't spend it (sell the IOU for goods and services). Everyone receiving the currency will do the same2. The economy slows down both directly through forgone purchases and indirectly through no investment in endeavours with a risk greater than zero.
Wouldn't the effect of this be to make the wealthy extremely risk-averse?
The wealthy are already extremely risk-averse. This isn't as apparent in a fiat currency as those currencies reflect (however poorly due to manipulation) the underlying economy3 where inflation driven by productivity growth, population growth and the price/wage spiral requires equity to be put into risky investments that outpace inflation. Indeed this relentless hunt by the wealthy for places to park money without the risks of normal productive investment created the sub-prime mortgage and financial derivatives market. And the counter-reaction of deflationary cryptocurrencies, when in practice honest propagation of risk information would have prevented the same crash.
So yes, a deflationary currency would allow the wealthy to better express their existing risk aversion.
Wouldn't this increase wealth inequality and make social mobility more difficult?
Both inflation and deflation entrench existing wealth inequality as the countermeasures require discretionary wealth to begin with. But while inflation forces the rich to continuously re-inject their wealth into society to keep it4, deflation requires them to hoard their money unless they just want to give it away. A lower and middle classes (i.e. those without sufficient assets to thrive without working) must spend what they earn and thus are essentially subsidising the rich in a deflationary economy; at the cost of their own social mobility.
1. A true post-growth society wouldn't need an expanding money supply. But then the key differences between specie and fiat currency would be irrelevant to an "economically static" society anyway. Money itself would simply be a token of energy or entropic appraisal with culturally-specific multipliers.
2. Except poor people living hand to mouth. Which is why widespread poverty is considered to be an excellent way to keep money circulating in an economy that would otherwise be deflating.
3. As more accurate currency price signals out-compete inaccurate signals over time due to exchange velocity and trustworthiness of face value; hence the slow and often belated but forward progression towards currencies that better reflect the global economy.
4. This doesn't make them any poorer as they own, to use a trite Marxist phrase, the means of production. But it does circulate the money which is a good thing. Consider it the objective of lending the serfs ploughs to work their allotment instead of hoarding the ploughs uselessly in the castle.
There is no hard fixed requirement that Bitcoin remain a deflationary currency.
It is possible - though perhaps not likely - that exchanges and mining consortiums will transform into (or be purchased as) off-blockchain central banks with the capacity to manage Bitcoins as a fractional reserve or outright fiat currency.
Yes and Yes + Caveat.