Well the reason we have these is because our 'system' of Western music is comprised of both whole steps and half steps. That's the way it evolved from Gregorian chant. (For we fretted instrument players, a whole step is two frets and a half step is one fret. It's a whole step from fret 1 to fret 3 and a half step from fret 1 to fret 2.)
So why are flats and sharps important ….? Well, to start with we need flats and sharps in order to have half steps and we need half steps in order to make music that sounds 'right' to our traditional Western ears.
OK, guitar players, try this: starting with C on the 2nd string first fret and staying on the 2nd string, play every other fret (whole step) until you reach C on the 13th fret. How does that sound? Doesn't it make your ears want to hear some half steps somewhere in there?
Also as a result of the evolution of 'Western" music is the fact that the intervals of fourths (C to F) and fifths (C to G) became very fundamental to Western music. (Without those intervals we wouldn't have all the three-chord songs that are so near and dear to our hearts.) You simply can't get from either C to F or C to G without using a half step.
Think that's complicated? Then don't ask me about double sharps and double flats!
So that's it; Western music 'needs' half steps … and you need flats and sharps to create them in every key but C and A minor.