In Star Trek why is there a kill setting on phasers?

In the creation of Star Trek Gene Roddenberry wrote the future society as a utopia. There is no need for money, there is no hunger and there is little to no violence inside of the Federation. I understand that there are weapons still - that doesn't seem contradictory to a Utopian society. Why is there a kill setting on phasers though? In a society that has advanced in all aspects, why would there be a need or desire to have a kill setting on a phaser? A setting that will immediately disintegrate anyone it hits. It seems not only counter to the society but completely unnecessary.

Now I am aware that it is used many times in different episodes as the only solution to certain problems but despite that I wonder why it's even a necessity. Some other solution may have worked just as well, but using the kill setting was easier. Also there seems to be nothing keeping anyone at all from getting a phaser and setting it to kill. Considering all of the different species and races they encounter it seems to go against the Prime Directive to even use the kill setting on a phaser. So why does that setting exist?

Answer

First, to quote yourself:

there is little to no violence inside of the Federation.

But outside, there is. There are Klingons, Romulans (depending on the series/setting) and other enemies, who probably won't be impressed with anything making them take a nap for a while.

Also, the whole setting isn't as pretty or utopian as you said. In Kirk's time they still use some kind of money (not really sure how it's called in the English version, but in German they call it ducats (which is rather odd, as most people here associate these with classic pirates/caribbean sea)).

Regarding the Prime Directive: The non-intervention part (killing or just talking) aims at species not being capable of reaching other civilizations (i.e. no warp drive or similar technology), so they're not influenced by them and to avoid things like sudden power shifts. Otherwise they would violate it, just by taking a trip out into space, but at the same time it's been a different Federation in Kirk's days.

But in general, I think it's just logical to have a kill setting as well, because more sooner than later you'll encounter bad guys, who won't mind getting taken out over and over again. Also it's been profen in more than one episode that it's possible to manipulate phasers so they become stronger or overload and explode, so not having this setting wouldn't really impact anyone wanting to actually hurt or kill people. Instead it just limits valid uses in case of self-defense (if you assume they're not out to hurt anyone intentionally) where killing your opponent is the only effective and viable reason.