Airavata served as Indra's mount, helping the sky-god release rain by shattering clouds with thunderbolts. In agricultural societies dependent on monsoons, elephants naturally symbolized fertility and abundance. Only well-watered, vegetation-rich lands could sustain these massive creatures. By receiving Airavata's head, Ganesha inherited this rain-bringing power.
Krishna is also used in the sense of "karshate iti Krishna"—meaning one who attracts. In Yoga philosophy, he is the presiding deity of the Ajna chakra. He attracts and pulls up Arjuna, who is stuck in the Manipura chakra. This is the essence of the Gita in Yoga philosophy.
In human lives, I have observed three main desires: wealth, power, and knowledge. I have one more—Rasa (The Universal Emotion). This desire is so intense that it can easily overshadow the other three.
