I don't know if it's so much about importance for English as importance for writing/literature. The right word to express a concept is about more than compactness.
I argue it's about both processing abstract ideas, and emotional content.
The latter case is simple--Perseverance, say, has a powerful immediacy and emotional persuasiveness that isn't conveyed by the denotationally-equivalent "tendency to move forward in spite of obstacles."
The former case is more complicated: the human brain can only hold so many things in short term memory. This is why phone numbers are broken into pieces. Long sentences with many ideas are hard to understand because there's much to piece together. A single word that does the same job as a handful eliminates this problem, because the brain can instantly recognize a complex concept with a single symbol.
Think about multiplication--technically, it's just adding one number to itself a number of times equal to the other number. That's already a much harder way to think about it than the shorthand, "multiplying." Writing out "2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2" is also much harder to understand and solve than "2 x 10."
Counterpoints: Op's line about "Obfuscate" and "Elucidate;" the idea that "fancy words" are hard to understand.
I'd like to point out that if conciseness is your goal, "Obfuscate" or "Elucidate" are probably not the words you'd choose. Absolutely choose a shorter word over a longer one if it means the same thing, unless you have a poetic reason not to. "Clarify" or "Inform" would do the job of Elucidate in all but the case that you need to highlight the root of "Elucidate" referring to light--ie, poetry again. "Obfuscate" can be covered by "obscure," "hide," "enshroud," "darken," "conceal"... the list goes on.
In the case you do have a longer word with no shorter equivalent, do we really want to dumb down our writing so that no one has to look at a dictionary or plunk a few keys in Google search? I'd rather expand minds when it's that easy.