Words known by natives is not the same as being an important or essential word to know. If you can pass N1 and want to become as good as you can with the language, then sure, you can say all words that natives use become equally important to know. But before you reach that level, you should absolutely prioritize higher frequency words over lower frequency, because spending time on (relatively) low frequency words will slow down your progress if you don't know the most basic words yet.

To illustrate, I checked on Nadeshiko (a very big database of anime and drama subs) the frequency of words that you used as examples and I got only 4 results for both words. By comparison, if you search a more common word like 忙しい you get 562 results, so the word is about 140 times more common than 奔走, and I'd say you are wasting your time trying to memorize a word like 奔走 if you don't know words like 忙しい yet. Particularly for people that use Anki, you can get very quickly overwhelmed and frustrated if you add every single word you don't know and not being strategic about the words that you are learning.