In terms of private banks, a basic savings account wouldn't really be a big risk for them nowadays because it's a bare bones account. It doesn't include things like access to credit cards or other forms of credits, or any form of long term investments.

If anything, banks might even like the idea, because it gives them a way to offload their riskier (and let's be honest less profitable) customers without making society fully collapse.

If the system is implemented properly it's a win-win for everyone.