Not enough words

One of the many reasons I still struggle with Japanese is the excessive number of homophones (words pronounced the same, but with different meanings). Often in Japanese one pronunciation doesn't just have two or three meanings, but 5-10 or more.

Consider “Kakeru” (one of a 1000 examples I could give):

It can mean 1) to break / be broken 2) to lack 3) to wane 4) to build 5) to be able to write 6) to hang / suspend 7) to put something on / cover something 8) to soar / fly 9) to run / gallop 10) to bet /gamble/ risk.

I suppose Japanese folks can discern the meaning from the context (I am usually in the dark there too), but it still seems awfully vague. The word-play opportunities must abound if you are clever enough, but it’s not so great for Japanese learners.