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The bank would have to make money from its other services instead.
At present, the ECB holds about 25% of EU members government debt.

This increase in the money supply is why QE can cause inflation.
The money created by the ECB would be that amount and nothing more.
Consequently, QE would be much less inflationary than today.

The debt benefit
So where does national debt fit in?
Indeed, this is how digital euros would be introduced into the economy.
However, you wouldnt just buy the same amount of bonds as you sold.

Interest rates and other questions
An added reason for doing this is interest rates.
Note that we can only take this medicine once, however.
As a result, EU states will still have to be disciplined about their budgets.
What if other central banks do not take the same approach?
Also, many countries would probably be tempted to take the same approach.