Mountains seems as special place for revelation (Mt. Sinai, Moriah , Sion) , acts of G-d , sacrifices and dwelling of G-d (as on Mount Zion , Jerusalem ) so it would very inappropriate for Elijah to kill false prophets there and there is also that he build altar at Mount Carmel .
Gen 22:2 God said, “Take your son – your only son, whom you love,
Isaac – and go to the land of Moriah! Offer him up there as a burnt
offering on one of the mountains which I will indicate to you.”
Gen 31:54 Then Jacob offered a sacrifice on the mountain and invited
his relatives to eat the meal. They ate the meal and spent the night
on the mountain.
Exod 19:12 You must set boundaries for the people all around, saying,
‘Take heed to yourselves not to go up on the mountain nor touch its
edge. Whoever touches the mountain will surely be put to death!
there are many more examples.
Good reason for brook(torrent) Kishon is that river very good place where blood would not defile the holy land as much. as it flows in to the Mediterranean and then to ocean. as further we read that lots of rain is coming and wash away the blood because it is probably empty after 3 years without rain.
Num 35:33 “You must not pollute the land where you live, for blood
defiles the land, and the land cannot be cleansed of the blood that is
shed there, except by the blood of the person who shed it.
Ezek 36:18 So I poured my anger on them because of the blood they shed
on the land and because of the idols with which they defiled it.