The core meaning of the verb けす is not "turn off" but is "put off (a fire)" or "extinguish." The gas stove is a recent invention (I believe from the 19th century) and before that, people used to say things like "たきび の ひ を けして ください" and "かまど の ひ を けしてください (=please put out the fire in the oven/furnace)," and you still here "たばこのひをけしてください” and “ろうそくのひをけしてください” So the expression in question doesn't actually mean "please turn off the fire of the gas." It's more like "please put off/extinguish the fire on the gas (stove)." If you think this is still too verbose, you can trim it into "ひをけしてください" by dropping the “gas” part, not the “fire” part.

they say that because they want to make every sentence they speak as real as they feel. Though these sentences might sound exacgrated at times.