As I noted in a comment, the description in this question of real world central banks is overly simplistic and misleading. Central banks do not make proportional changes to the monetary base to set the price level. However, I will ignore those problems, and just address the core of the question: does it make sense to change account balances on a pro rata basis to keep the price of a crypto currency stable?

Such a policy would have no benefits for holders of the currency. Imagine that the currency lost 10% of its value in trading one day, and so holders have a loss of purchasing power. If balances are reduced by (approximately) 10% to balance this, even if the currency returns to parity, you still lost 10% of the value of your holdings, since you have 10% less units.

This would also make any contractual obligations extremely awkward: any contract involving future payment would have to take into account the change of base. All transfers would have to effectively cease before the redenomination of accounts, in order to inconsistencies. If contracts do not take into account the change of base, you have no idea whether you can meet a future obligation. If I have \$100 in a bank account, I know that I can make a payment of \$90 next week, and could plan around that. If account balances are changing in an arbitrary fashion based on the exchange rate, I can no longer plan ahead.

As I noted in a comment, the description in this question of real world central banks is overly simplistic. Central banks do not make proportional changes to the monetary base to set the price level. However, I will ignore those problems, and just address the core of the question:

1. Will it make sense to change account balances on a pro rata basis to keep the price of a crypto currency stable?
2. Will “seigniorage shares” work to stabilise the currency value?

I will cover each of these in turn.

1. Pro-rata change policy would have no benefits for holders of the currency. Imagine that the currency lost 10% of its value in trading one day, and so holders have a loss of purchasing power. If balances are reduced by (approximately) 10% to balance this, even if the currency returns to parity, you still lost 10% of the value of your holdings, since you have 10% less units.

This would also make any contractual obligations extremely awkward: any contract involving future payment would have to take into account the change of base. All transfers would have to effectively cease before the redenomination of accounts, in order to inconsistencies. If contracts do not take into account the change of base, you have no idea whether you can meet a future obligation. If I have \$100 in a bank account, I know that I can make a payment of \$90 next week, and could plan around that. If account balances are changing in an arbitrary fashion based on the exchange rate, I can no longer plan ahead.

If the overall “market capitalisation” of the currency had a tendency to be stable, pro-rata changes might keep the value of the unit stable. But of the “market cap” is changing, the value of the unit would still change, but not as much. However, this is just cosmetic, like a stock split.

2. I will admit that I have not read the linked paper on seigniorage shares, but I doubt that any such scheme could work, based on the description provided. The description given here states that developers create a “central bank” that issues the equivalent of Treasury bills to create an interest rate in the crypto-currency in order act like a real world central bank using interest rate policy. The problem is that real world central banks make seigniorage profits by buying Treasury bills issued by the fiscal arm of the government (the Treasury), and the Treasury is paying the interest. The Treasury can do this because it receives tax revenue, future tax revenue backs the interest stream.

The crypto central bank has no tax revenue. It can only pay interest by “printing” more currency units. The more interest is pays, the greater the future dilution of the crypto-currency. This does nothing to make outsiders believe that the crypto-currency will be more valuable in the future.

The only way such a scheme could help stabilise the value of the crypto-currency is that the “central bank” was engaging in activities that were in some sense profitable, so that those “profits” would cancel out the dilution that results from interest payments. For example, it could levy a small “network fee” on transactions (which is the sort of tax I believe that crypto-currency backers want to avoid). However, it is safe to say (based on equity market price volatility) that profit expectations are hardly stable, and so the value of the crypto-currency would change as “profit” expectations change. Since raising the rate of interest paid by the central bank will not improve its expected profitability, it would not be in the analgous position of a real world central bank, which is increasingly profitable as it raises interest rates. As a result, there is no reason for a crypto interest rate policy to act like real world interest rate policy.