Chaos Signals to Decide Blockchains?
The main issue with choosing a miner "at random" is finding a verifiable public source for randomness. Most public randomness sources run through a centralized party, which is no good for Bitcoin, where everything needs to be cryptographically verifiable. 

There have been some attempts at a public, verifiable randomness source in Bitcoin, but given that the system is eventually consistent and subject to collusion, it's been shown to be difficult. See "On Bitcoin as a public randomness source" and "Proofs-of-delay and randomness beacons in Ethereum".

Another possible way to avoid the issue of excessive energy consumption is Proof-of-Stake-based blockchains. Instead of creating a computational marketplace (which in Bitcoin is very competitive) to verify blocks, proof-of-stake uses staking of coins to decide what the next block is. You earn a block reward by committing money to a certain block. There are chain-based approaches (Peercoin and Blackcoin) and BFT-based approaches (Casper and Tendermint). Here's a good intro guide to PoS and Ethereum's Casper.