In addition to the fee they are leveraging your deposits - and European banks are no less risky for the depositor than the US ones (just look at the 2008 era). Having a 'true bank' that does not leverage your money and has no investment risk would probably be useful to a certain segment of people but the assets would still have counterparty risk and everything else so in the end a very niche market since the best way to handle risk is to distribute to multiple counterparties, currencies, etc... and then you might as well get the interest from the money at that point since you've de-risked so much already.
Since 2008 EU banks have gotten more stringent requirements per regulations compared to the US, the degree of additional risk is hard to know for sure without a large scale collapse.
What are you basing this on? What are some of the ways EU banks (does it not vary by country?) have gotten more stringent requirements per regulations compared to the US?
In the UK, banking is normally free, but on the continent, you normally pay for the account itself and any cards you may hold. Some banks may offer fee waivers for those whose salaries get paid into the account, or if you have a cardless account etc, but it is fairly common practice to charge a small fee for the bank account itself.