Why have proof of work?
You have the right idea when you wrote:


  allows multiple parties who don't trust each other


Then you proposed:


  just have one miner who publishes...


That would mean that everyone has to trust and rely on that one miner to publish accurately and correctly. 

But the whole point of the system is to not trust anyone.

Proof of Work (POW) is the mechanism that creates a trustless system without any central node.


P.S.  There are potentially lots of ways to tamper with a block chain other than forking.   There are double-spends, re-writing old transactions, forging new transactions, and denial of service attacks.  So far, the POW scheme seems to be an effective defense against all of these attacks.