I don't think there's any purpose behind it, most like early on, game with shooting were just simpler to develop, especially with regards to limited processing power and storage. For example I remember an extract from a review on the original Doom, saying that it would be much better if they were able to talk to the monsters; but at the time, a talking game would have been nearly impossible to make, especially to the same level of polish as the original Doom.

And then it's a feedback loop: video games get the reputation of being violent (perhaps undeservedly so, like Myst was outselling the original Doom, IIRC, but violent games made for bigger headline in mainstream media) => only people interested in that buy them => violent games are the best-selling => games...