The words "concern" and "worry" aren't different levels of business/academic english, but rather synonyms that actually have different meanings in different contexts.

Your question is confusing. 

How to or Why learn new business English words. (when there are lots of simple ones available)? 

Learn those words in a paragraph, repeat that particular phrase out loud 5-10 times until you can say it fast. 

Have a convo with your language partner.

Memorising and being able to use them spontaneously need different ways of practicing.

For long term memory, our brain needs to grasp the full context and not partial. You know that.

Make detours, it's the best shortcut for some people and things. :)

I can give you two tips that I have found helpful when learning new languages.

One tip is to look for similarities between the words in the new language and the words in a language you already know. I am a native English speaker, and English has a lot of words that come from either German or Latin words. For example, I know what the English word 'cow' means and it's very similar to the equivalent German word 'Kuh'. Similarly, it's easy to to remember the French word 'jalousie' if you know the equivalent English word 'jealousy''.  You have to be a bit careful because some words that look like they should be similar don't mean the same thing in different languages( 'journée' in French, for example means a day and is not related to the English word 'journey' although they look similar), but in general I find looking  for similarities helpful.

If you are learning a language that doesn't have similarities in vocabulary with your own (and I think that may be the case for you with Kazakh and English), then the second  tip I can give you is to write a sentence when you learn a new vocabulary word. I have been doing this for years now while learning Chinese . When I encounter a new Chinese word, I write a sentence using that word and when I revise vocabulary, I read the sentences rather than studying individual vocabulary words. I find that, rather than remembering single words,  I remember the sentences and I know how to express the idea in the sentence properly without having to search my memory for the individual words. 

I should also mention that I regularly show my Chinese teacher my new sentences and she helps me correct them so that they use natural sounding Chinese the way a native Chinese speaker would speak. If you don't have an English teacher to look at your sentences, I would suggest posting them here on italki and asking native English speakers to correct them for you.