Why are short sentences and short paragraphs appropriate for business communication?

I wouldn't say that is always true, but I agree with the general idea.

Here are a few thoughts.

'Short' often means clearer, more direct and easier to understand.

It's not uncommon for business people to write poorly. As the sentences and paragraphs get longer, the problems often increase. 

Business readers appreciate writing that does not take a long time to read.

Business writers often think that writing 'long' makes their writing seem more important. Smart business readers realize that it does not.

Best wishes, Clive