That just indicates that it's regulated. Where's the "over" part?

Personally, it sounds like a rather good idea to have regulation over who's allowed to use the word "bank", given the assumptions that the general public will make about anything with "bank" in the name.

In one system, thousands of people are scammed out of millions of dollars every year.

In the other system, a company that is not a bank was forced to avoid the word "bank" in their name.

This sounds like two reasons the second system is better, to me at least?

Can't see much of an issue with random businesses not being able to call themselves "Bank" personally.

Would you also agree that any random company should be able to label themselves a hospital, pharmacy or university? If not, then there's your answer.