Proof of work and mining systems are actually pretty far from being fair regarding transaction ordering. On the one hand the miners in validators in a Proof of Stake system work as local dictators on the set of transactions, meaning that they can select which transactions are put into the next block. This gives on the one hand the possibility to censor or delay certain transactions. How big this delay might be depends on the competition and collaboration of the miners and validators. On the other hand, as the transactions are usually processed based on transaction fees and miners certainly priories the transactions with the higher transaction fee. This gives the possibility for an average user to game the system, in the sense that it can be sure that a higher fee transaction will be surely prioritized over a lower transaction fee, giving for instance the possibility for a successful double spending attack.
It is an open question if a blockchain protocol can designed in a fair ordering way. Other distributed ledger technologies like Hashgraph has the fair ordering property.
