Ah, Super Mario, champion of the Mushroom Kingdom! A hero among men (Toads, Birdos, Yoshis, Boos, Goombas, Koopas, and Dolphins too!) He has selflessly rescued the Kingdom more times than I have fingers. With the constant threats of invasion by the dastardly Bowser, King of the Koopas, it's kind of a wonder why Mario hasn't slain the beastly dragon lord. That would put an end to his doings once and for all, wouldn't it? No more Bowser, no more threat, right?
Wrong.
You have to remember that Bowser is a king, and while most of the series is focused on and in the Mushroom Kingdom, the Krowned Koopa King does rule his own country (I avoided calling it a kountry because I'm mature.) known to most outside inhabitants as the Dark Lands. This country of fire and brimstone, swallowed in darkness by a cloud of black smoke so thick it chokes out the sun, is one of the largest areas on the planet, consuming an immense portion of the world to the approximate West of the Mushroom Kingdom.
This country is home to some of the most spectacular features on the entire planet, such as an entire ocean made of what appears to be blood (many confuse this as lava, but it is swimmable. It could possibly be water colored red by the lava pits all around, but that seems unlikely.) And, despite its harsh conditions, it seems to be readily hospitable to a number of the planet's primary species. For instance, Koopas, which probably originated in the area, are able to live without their skin and so can continue life after falling into one of the lava pits.
What does this have to do with Mario not killing Bowser once and for all? Well, you see, when a king dies there is a sort of power vacuum, and that needs to be filled. You'd think the Mushroom Kingdom would assume control of the Dark Lands once its ruler was defeated, but they have more than enough muscle power to take it with no casualties on their part. It's evident they don't want it. Who might want it? Well, King Bowser has behind him eight little heirs who would all eagerly accept the position. If only they could decide who.
But these aren't reasonable Koopas, ladies and gentlemen, these are masterminds of evil. Unlike their father, who is quite frequently shown to be in reality a compassionate, caring, and loyal King with a heart of gold, the Koopalings were raised in the face of constant war. They understand nothing but heartache, death and misery. And they utilize these twisted facets of their personalities to concoct traps and prisons far more devilish than Bowser would ever even want to. And in the face of their father's death they would use these on each other. The Dark Lands would be thrust into civil war, and countless lives would be tossed away as one faction battled for control of the whole cake.
Mario can't kill Bowser because doing so would result in the deaths of millions of innocent lives. What kind of a hero would do that?