The government wants money to flow, to drive the economic growth and job creation that gets it reelected. It's the last thing that's going to encourage low-consumption/high-savings lifestyles.

Unless you pay upfront for the service rather than having a free bank account.

If your economical model is to take advantage of people going overdraft you can be certain the bank won't try to help clients. If the bank can make more money by having clients with more money that would probably work better, now I'm not sure how that would scale.

Banks does make a lot of money if the customer spends his money or stores his money using the services of the bank.

Except didn't they charge the same ridiculous fees even when the accounts were not free?

Banks don't want you to spend money. They want you to have as much in your account as possible. So it would be in their interest to encourage saving.

Pretty sure they want you to pay as much interest and generate as many interchange fees as possible.

This. One of my friends got a call from his bank trying to get him to sign up for a car loan because he had 30k € in his bank account and should "splurge" a little.