For society, this is really important. Basically everyone needs a bank account. In some countries, the government even forces people implicitly to have one in order to pay taxes or fees.
In such a case, the government should provide a solution for this too.
Then, there are also economic implications of this. Society needs to run many banks, which uses a lot of resources (especially people). However, many people and companies only need one simple part of banking: cashless payment. Something that’s, from a technical perspective, just a database for transactions and accounts. So a default solution by the government makes sense to me.
Of course people will argue against this as the government would have full control over people’s money. But I think that’s the case anyway. Money is something inherently governmental as it’s produced by an governmental institution (central bank) and collected by the government in form of taxes.