The approach can go both ways I think. I know some people from undergrad who were all about diversifying their schedule, getting minors or even dual majors in subjects they had no professional interest in, they were just curious. And I think they were a lot better off for doing so. But likewise I know other people who got so dragged down by worrying about these secondary classes that they weren't able to put their best foot forward in their major's core classes (like a mechanical engineer who half-asks his engineering design capstone because he's so worried about passing his Chinese test).
I feel it comes down to what environment you learn the best in. If you're disciplined enough to learn a language or say a soft science on your own time, then I'd recommend that, it's a lot cheaper/more flexible than a classroom setting. But if you need the pressure of grades/tests to push you, then maybe you should go for the diverse schedule, as long as you don't sacrifice other things.