Here's one example: Old English had plenty of good words like cow, pig, and sheep. (Or their Old English counterparts of course) and we adopted the "foreign" (Norman) words boeuf, porc and mouton. In French they still only have one word for the animal and its meat, but since we adopted these foreign synonyms, we now have these lovely nuanced words beef pork and mutton and we can say something like "sheep meat" much more succinctly and elegantly.
"Soup of the day" has a different connotation than "soup du jour," don't you think? Isn't one more elegant, conveying a sense of fine dining culture (even if it's not always used that way anymore)? It's subtle, yes, but it's that subtle nuance and our huge vocabulary that makes English beautiful.
Not to mention the fact that a well-read English speaker also has a mastery of a lot of basic foreign phrases and has that much more the advantage when communicating in another language. We had Anglo-Saxon ways to say information, pensive and ridiculous before the Normans showed up, and I'm sure we would communicate just fine if we still used them. But now, any student of French can tell you how handy it is to be able to read a foreign text and not have to look up ever single instance of information, pensif and ridicule. Any student of a non-cognate language can tell you how much more difficult it is to achieve literacy when you don't have that advantage.
The human brain is capable of absorbing and using a lot more information than we give it credit for. Why limit ourselves in the name of efficiency when willingly educating ourselves can open up so many realms of opportunity? I promise you that none of the foreign words you've acquired over the years are sitting there wasting valuable storage space in your cerebral cortex.