I can think of tons and tons of Japanese words that have (so far as I know) nothing whatsoever to do with Chinese. There are several classes of kanji use in Japanese; some are compounds based on on'yomi, sure, but some are just kanji thrown in for the way they sound, and some are traditional Japanese words with the same meaning as the kanji.
You need to understand kanji is just another writing system. A lot of people in the West fail to recognize this and instead end up believing that kanji are "works of art" or some such thing, or that it is used in some specialized way or has some kind of special properties. But the simple fact of the matter is that this:
七面鳥
...is just how you spell "turkey". There's nothing more to it.
When you understand this basic fact, it's obvious why you would never want to "create your own word" from kanji, just like you wouldn't want to "create your own word" from Latin script. The most you might want to do is create a name for something in a fictional work, which of course you can do with kanji just like you can do it with Latin script, for instance.