Why proof of work rather than posting to a public forum? I understand that proof-of-work plus a block chain is one way of creating a trustworthy public ledger of transactions.  But holy hell, the cost to society in terms of energy consumption is VERY high per transaction.  I participate in conversations online all the time where I implicitly trust that I am seeing the full discussion and that everyone can see my input.  Usenet, for example, does this in a decentralized way.  Couldn't we just post our transactions to usenet save some resources?
I participate in conversations online all the time where I implicitly trust that I am seeing the full discussion


Proof-of-work is one part of what allows bitcoin to be trustless, which is a very important property for any decentralized system of value. If transactions were just posted to a forum, then what is to stop a forum admin from editing, censoring, or deleting transactions? 

Creating a trustless financial network is not a trivial task, the large amount of energy being spent to secure the network is a testament to the value users see in maintaining and participating in the network.