Why aren't public-private keys sufficient to build a block chain? Why do we need proof of work/stake?
Since Blockchain is a decentralized system, it has to stop malicious behaviour [which may just be disruptive if not benefiting the attacker directly] and collusion.
Proof of work achieves that by introducing a very large computational cost.
It also removes the burden on the nodes of checking transaction ordering. Also the code is running in parallel in multiple nodes so how is theany transaction ordering going to be universal without local copies being different?