Mining isnt about processing transactions, it is about fairly distributing coins and preventing anyone from cornering the market.
How does mining accomplish this? Last I checked most coins are falling into the hands of financially well off miners with huge mining farms. Massive capital investments are now needed to run a profit mining, it's a system that only allows the rich to become richer.
What is your alternative? Let a single institution print them at whim?
Also, the electricity costs are not paid by anyone but the miners. They are also forced to sell coins to pay bills, thus making coins more affordable to us proles.