Straying away from anything more English class-ey, let's explore everyone's favorite word:
Gnarly
When you hear "gnarly" you probably get some IMAGES of California surfer dudes with blonde hair transferred into your BRAIN (but obviously if we don't see the same pictures, I've got you with some gnarly videos). "Gnarly" (in culture) generally has two definitions.
1) Something gross/gnarled/repulsive
2) Something impressive/incredible/ground-breaking
If "gnarly" had only one meaning, where would all the fun be in life? You wouldn't know if I was talking about bot flies coming out of peoples eyes or Danny Davis using all his money to shift snow around and invite the greatest (living) snowboarders to give their chops a go. Think of the adrenaline rush!
So besides making your life more confusing/annoying/difficult to use Google Translate/whatever, words having two meanings makes the world more exciting. Obviously "gnarly" is a very shallow example, but if you go into poetry, the double meanings of words don't make it more confusing, but add twice as much imagery to half the character count. It makes language an inconvenience on a surface level, but the ambiguity is what changes it from a grammatical formula to a form of artistic expression.