... Also there are a lot more languages in Acrobat DC then in Indesign. I found it quite disturbing considering that InDesign is used to create and format documents.
Your final sentence explains it accurately. Some writing scripts and languages have very different sets of rules – Chinese, for example, allows text to run either horizontally or vertically, and design-wise, it's very grid-based. Hebrew and Arabic text runs right to left.
But even for "Latin-based" languages only, InDesign needs a lot of information on the peculiarities of each language, to be able to spell check and hyphenate for example. And that is because you use InDesign to create and format documents.
The "language" selection in Acrobat doesn't really do something -- all it does is setting the identifier of a certain text to that selected language. It does not translate, reflow, alter, re-set, re-hyphenate, or otherwise change anything in the displayed text itself.
Yes. I did. Exactly my point. As I am formatting and designing documents in various languages I found it difficult to set proper language for a specific text. Sometimes because the language cannot be set I am forced to set No language to entire document and then to go into Acrobat DC and set the right language.
It is important in case your PDF will reach people with disabilities see Read Out Loud or Accessibility Setup Assistant. In that case it is important that the language is set properly. So, I guess setting a language in Adobe does really do something.