Would not proof-of-stake be an algorithmic calculation, available to anyone with the dataset (blockchain) and the computational power? Right now certain credit

Would not proof-of-stake be an algorithmic calculation, available to anyone with the dataset (blockchain) and the computational power? Right now certain credit card companies charge a fee for calculation of a credit score (at that instant/ on the fly). Presumably in a cryptocoin economy everyone who has access to the dataset and knows the formula could tell you the proof-of-stake. Banks historically act as a time-throttler on transfer of funds, making sure the economy does not move without the inner cogs of the banks turning first. It is widespread now globally. With a cryptocoin economy, banks would not throttle time any longer and would instead help facilitate additions to the blockchain (via fee) as many exchanges currently do. What all factors does one need for proof-of-stake?