What you are proposing is generally illegal in the U.S. Companies are allowed to snoop on non-encrypted web traffic, because there is no expectation of privacy, but different standards and rules apply to encrypted sites, i.e., including banks.

Also, since bank websites and email are the most frequently accessed encrypted sites, a company would be exposing itself to ruinous liability if a data breach led to the release of private employee information, i.e., bank records. No company would take on that sort of liability, and you can bet that any competent legal counsel would make the company aware of this before they implemented something like this.