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.