Why proof of work rather than posting to a public forum?
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.