When we say " he has written many books" it does mean that he began in the past writing books and goes up to now , but it does not say that he will write another book or if he is not dead he will obviously write another book So why don't we say" he has been writing some books" (which indicates clearly that the action is not complete and still in progress)
"He has been writing some books" says nothing about whether any were ever completed. It does suggest that the process of writing is still ongoing, if not actively write at that moment.
"He has written many books" says that those 'many' books have been completed. It says nothing about whether the process of writing is still ongoing.
I am not aware of any way to say, with such a simple clause, both that books have been written in their entirety and that he is still writing books. If you wish to communicate both facts clearly, you need two clause. "He has written many books, and has been writing more" is imprecise and might not strike anyone as beautiful prose, but it conveys both meanings.
Here is my take on it.
The present perfect and present perfect progressive put the past in relation to the present not the future.
Depending on what you want to say or emphasize you either use the present perfect or present perfect progressive.
If you want to emphasize the duration of an event, you use the present perfect progressive.
"I have been playing the piano for an hour. Can I stop?" (single action, that started in the past and has continued up to now.)
"She has been playing the piano since she was six. No wonder she's so good!" (repeated action. A habit/action, that started in the past and has been repeated since, over a period of time that goes up to now.)
"What have you been doing?" - "I have been watching TV." (recent activity - single action)
"I need a holiday. I have been working very hard recently." (recent activity- repeated action)
The present perfect progressive doesn't give you information about if or if not an action will continue in the future.
"Why are you crying? I've been reading your book. It's so sad..."
The person talking is emphasizing the activity. We don't know, if the person will continue reading or not. He/she might just stop there and never ever finish reading the book. Or perhaps she has just finished reading it. e.g. I've been reading your book. The ending is so sad."
"He has written some books."
You are talking about several completed actions that happened in a period of time that started in the past and has continued up to now.
"He has been writing some books."
You are emphasizing the activity. The author may have never finished writing any of his books. Will he continue writing? - Who knows.
In addition to re_nez excellent answer I'd like to say: "He has written some books" focuses on the completed action, the result, these books have been completed. The present perfect is also used when we want to express how much or how many: "He has written 5 books".
If you have just finished reading a book, you can also say: I've just read your book, the ending is so sad".