I disagree. It's only broadening in the additional people it allows you to commune with. Other than that, it's a waste of time.
Having to convert between languages (I'm a native speaker of English who lives in Germany) all the time is huge overhead, sort of like if every country had its own system of measurement, except that the overhead is incurred much more often, not just for measuring things.
There are subtler benefits - I speak three languages natively, and the part I love most about that is also the part that frustrates me most. Afrikaans is a modern language and has a relatively small vocabulary. Insulting someone therefore consists of creatively stringing together colourful combinations of everyday words, mixing in the odd English, Malaysian or Zulu word, and then spoken with a religious fervour that cracks you up. It's side-splittingly funny. What frustrates me is that no other language can do that, so I can't share that with my girlfriend, who is French.
German has similar mannerisms about it. It's naturally dry in a way that English, for all it's adjectives, can never hope to be.
To give you another perspective, I've always had a few deal-breakers I look for when meeting a girl I might otherwise be interested in. First, she needs to speak more than one language. Seconds, she needs to have spent a significant amount of time outside her own country. She must either be able to ski or snowboard. Last, she needs to be able to play a musical instrument. Beyond that I couldn't care less about race, job, creed, colour or any other bigoted perspective.
To know another language is to know another world.
In 1984, newspeak was all about removing ways to describe things the Party didn't want the public thinking about, so that in several generations of the language nobody would be able to comprehend dissent. And it actually has some real life foundations.
Just think of all the times a foreign language speaker says "I can't accurately represent this in whatever other tongue".
Note, I only know English, and after 6 years of Spanish throughout high school and college I have forgotten every wink of it. You really need to immerse yourself in a language to really dedicate it to memory, and constantly use it. Which is really a ton of overhead, that isn't really necessary, I agree.
German, for example, has no word for "silly", while English has no word for "gemütlichkeit".
Eliminating the overhead is worth any of these sacrifices, though.
Language structures our thoughts. It is claimed that Chinese are better at math because of their language structure. How you express things in a different language will help you more clearly see the concept in your own language. I learned more about English by learning German than I did in all my schooling. It improved my spelling as well because it made me understand the words I was using better.
It's VERY good. But skip the first 3 minutes of boring intro.
For broadening experience, see:
And for intellectual delight, see: