Posting the full chapter IV here from A Conflict of Crypto Visions, Why do we fight? A framework suggests deeper reasons, here is contains an interesting POW/POS section:
Episode IV: Proof-of-work vs. Proof-of-stake
Bitcoin’s proof-of-work is an embodiment of the constrained vision, a mechanism to work around fundamental limitations rather than re-engineer them. First explained by Nick Szabo in Money, blockchains, and social scalability , Bitcoin’s proof-of-work accommodates our cognitive limitations and behavior tendencies by making a necessary and intentional tradeoff: greatly sacrificing computational scalability to improve social scalability.
A feature to the constrained, a bug to the unconstrained.
The ability to participate in an “institutional technology” is predicated on the technology motivating participation and protecting the system and its participants from malicious activity. By improving social scalability, which proof-of-work does so effectively, the number of people who can beneficially participate in the system is maximized. Therefore, the constrained, “proof-of-work” vision posits that Bitcoin’s success should not be determined by its computational efficiency but by its ability to increase social scalability through trust minimization.
What the unconstrained vision deems computationally inefficient and unscalable, the constrained vision not only deems an intended tradeoff, but a fundamental feature : specialized, dedicated hardware should perform a function whose sole output is to prove that the computer did indeed execute a costly computation. As Nick Szabo highlights, “prolific resource consumption and poor computational scalability unlocks the security necessary for independent, seamlessly global, and automated integrity.”
While an implementation of both computational and social scalability is optimal, the constrained vision acknowledges that it cannot be done without compromising security. Embedded in computer science is a fundamental understanding of tradeoffs in security and performance where inevitably, automating integrity requires high resource utilization. Even with breakthroughs in computer science, the constrained vision recognizes that total integrity and absolute trustlessness is infeasible, making the delicacy of explicit and intentional tradeoffs all the more imperative. As such, the constrained vision fully accepts that such tradeoffs are unavoidable, and “it is probable no such big but integrity-preserving performance improvement is possible.” 
To the unconstrained vision, the assumptions around proof-of-work are entirely different. Instead of asserting that proof-of-work sacrifices computational inefficiency for social scalability, the unconstrained vision asserts that proof-of-work unjustifiably consumes significantly more resources than it creates, making it a wasteful and archaic system in dire need of improvement.
A commonly used statistic the unconstrained vision employs to illustrate proof-of-work’s “wastefulness” is a measurement of the amount of energy the system expends as a proportion of the total transaction volume the system processes. By employing such a statistic, it becomes obvious why under the unconstrained view, proof-of-work is so scandalously inefficient: “Bitcoin consumes five Hiroshima’s worth of energy per day” only to process “a mere fraction of what a payment service like Visa processes.”
The use of this argument to illustrate proof-of-work’s wastefulness implies that trust minimization is not viewed as a necessary feature in the unconstrained vision. If it were, comparing Bitcoin to Visa would be futile: Visa does not provide the same improvements in social scalability through trust minimization precisely because it is more “computationally efficient”. Such a comparison not only dismisses the existence of limitations, but attempts to associate two completely unrelated variables (i.e. energy expenditure and transaction volume are not functions of each other). As Sowell highlights, wrongful association of these variables leads to “statistical extrapolation without any analysis of the actual processes from which these numbers were generated.” 
A costless alternative?
Deeming proof-of-work wasteful suggests a cheaper, more prudent alternative exists. To the unconstrained vision, the reason proof-of-work has not fully succumbed to an alternative may come from a lack of care for the environment or a lack of imagination of technological advancements as Emin Gun Sirer suggests:
100 years from now, future generations will talk about the PoW craze with the same bemused view we hold for other mass manias. The absurdity of wasting energy to make chicken scratch marks on an electronic ledger is going to become more obvious. We are going to look back the same way we look at the use of CFCs and leaded gasoline. We should replace it with systems that can do better.
As previously highlighted, the unconstrained view is to remove specific negative features in the existing situation to create a solution. In the context of proof-of-work, the question posed by the unconstrained is then: “how can we remove the computational inefficiency and energy wastefulness of proof-of-work to create a better sybil-control mechanism and consensus algorithm?”
Attempting to answer this question, mechanisms like proof-of-stake have emerged as the most popular solution, as Ethereum’s Vitalik Buterin highlights:
“The philosophy of proof-of-stake is not ‘security comes from burning energy’, but rather ‘security comes from putting up economic value-at-loss’.
In a proof-of-stake system, a blockchain appends and agrees on new blocks through a process in which anyone who holds coins inside of the system can participate and the influence an agent has is proportional to the number of coins (or ‘stake’) it holds. This is a vastly more efficient alternative to proof-of-work ‘mining’ and enables blockchains to operate without mining’s high hardware and electricity costs.”
Under the unconstrained view, proof-of-work is classified solely as a sybil-control mechanism. As such, there is greater justification for removing energy spend on coin production. Emin Gun Sirer explains:
The energy spent on coin production is purely wasted, it provides no price floor for coins, it is value leaked out of the system. Much like how the high cost of printing Bahts doesn’t guarantee value higher than USD. It’s just the cost of competition between miners.
Thus, the goal in the unconstrained vision is to implement an inherently costless system without leakage. In proof-of-stake, network participants are not required to use inordinate amounts of energy to maintain ledger immutability, significantly reducing labor intensity. A reduction in labor intensity would be more fair and help encourage community participation due to lower barriers to entry. Specifically, the unconstrained vision claims that taking mining out of the hands of entities with access to excessive amounts of low cost energy would help redistribute the work evenly and lead to a more democratized system. By removing the feature that secures value in a proof-of-work system, security in turn is derived from the value stored within the system itself. As David Yakira notes, “in a sense, a PoS system is recursive, augmenting the value it stores implies better security which further allows the value to increase and so on.”
Under the constrained vision, however, defining proof-of-work as merely a sybil-control mechanism is non-exhaustive and trivializes its purpose. Proof-of-work is also seen as essential for maintaining unforgeable costliness “giving digital blocks real-world weight” and enforcing a predictable, meritocratic distribution mechanism.
Because the constrained vision believes there to be “no solutions, only tradeoffs,” a costless mechanism without leakage would also be definitionally impossible, as Paul Sztorc notes:
“Switching the payout-trigger to a social or political dimension would merely transpose the work-expenditures correspondingly to the realms of bribery and propaganda.
If an object has value, people will spend effort to chase it, up to whatever the object is worth (MC=MR). This effort is also “work”. [Thus], a stable solution to these problems is definitionally impossible , as there is always an incentive to work until marginal cost equals marginal revenue.”
The Future Remains To Be Built
As we’ve highlighted, these divisions between cryptocurrency enthusiasts, investors, and builders can be seen across the “unconstrained” and “constrained” axes, two conflicting ideologies that transcend geography, professional associations, or backgrounds.
We believe that the most likely outcome after the full possible actualizations of these visions is convergence in some form. While the future remains uncertain, a conflict of visions persists because in reality, visions are all we have to focus on ahead of a multi-decade roadmap of adoption and integration.