This reminds me of a call I got from Schwab, which is my brokerage and one of my two banks where I keep checking accounts as well. I had a bunch of money that I had transferred in and stupidly, lazily, just left sitting around earning basically nothing. A nice guy called me one time and pointed out that I could be earning a few hundred bucks (maybe $800?) a month just by putting it all into a very safe money market fund. I did do that (and also got around to investing most of it at a later date).

I'm sure Schwab would rather me have my money in a mutual fund than have a bunch of cash, for the reasons the other commenter pointed out (more complex arrangements and a view of the bank as a partner rather than an interchangeable "money box" is 'stickier') but this was a real double win for me and one of the handful of stories I call upon when I am asked why I do most of my financial business with that company.