Proof of work has nothing to do with blockchain itself. In Bitcoin, POW is how new blocks are found, but blocks are just payloads stored in the chain. Other, non-currency data can (and is) be stored in the Bitcoin blockchain, and this data does't necessarily require POW.

Bitcoin POW chunks might as well be new prime numbers; you spend a bunch of processing to calculate new primes, then you digitally sign the data and store those on the public blockchain and now you have digital currency. A blockchain block itself is no more CPU intensive than what it "costs" to set up a new SSL connection to whatever porn site you're browsing. It's literally just a chain of blocks of data hashes (even cheaper than your SSL connection) than include a previous block's hash, and which are signed.

POW is part of the cryptocoin part; blockchain is entirely unrelated - it's just a publically verifiable audit log (in this case also encapsulating the signed data).

There even exist cryptocurrencies which are not based on POW and the entire argument about environmental impact falls apart. Those have less environmental impact than Fortnight. But, in most cryptocurrencies there needs to be a mechanism to prevent people from arbitrarily printing cash and devaluing the system; aside from POW, staking is popular: you just buy coins outright. There are other methods; but in no case does the technology of blockchain involve POW.