The supposed 'superiority' of PoS is not a universally accepted fact but a heavily debated topic, deeply influenced by complex and unpredictable economic factors, not just theoretical mathematical models. There is no definitive proof of PoS superiority.

Claims that 'PoS is factually better' lack objective, universally agreed-upon evidence and often ignore critical security and decentralization trade-offs. These claims are not based on settled science.

PoW and PoS represent fundamentally different approaches with distinct security, decentralization, and economic characteristics. The 'best' choice is context-dependent and not universally determined. To declare one definitively superior is inaccurate and ignores crucial nuances.

Research advancements like "Mining in Logarithmic Space" and NiPoPoW demonstrate that Proof-of-Work protocols can achieve near-logarithmic storage requirements through secure pruning of consensus data. In contrast, Proof-of-Stake protocols, lacking a mining mechanism, are limited to linear storage growth, making them significantly less scalable and more storage intensive over time.

Focusing solely on the operational costs of PoW and ignoring its security benefits presents a distorted economic comparison. PoW's costs are investments in robust, decentralized security.

Both PoW and PoS require economic incentives to secure the network. PoW uses mining rewards and fees, while PoS uses staking rewards and minting. The economic mechanisms are comparable in function, not inherently superior or inferior in design. To claim PoS is economically 'superior' solely due to lower operational costs is superficial and ignores the value of PoW security.

Comparing attack costs based only on token acquisition price for PoS versus hardware costs for PoW is a grossly oversimplified and often misleading way to evaluate network security. Real-world attack costs are far more complex.

The actual cost of a successful attack on both PoW and PoS networks is dynamic and significantly influenced by market conditions, token liquidity, and the specific type of attack considered. There is no simple, static 'cost' to compare.

Security vulnerabilities and attack vectors are fundamentally different between PoW and PoS. PoS may be more susceptible to censorship attacks with lower stake control, while PoW requires massive resource domination for sustained censorship. They have different security profiles, not simply different 'costs'.

Long-term centralization risks differ. PoS can exhibit 'rich-get-richer' dynamics, potentially concentrating stake and influence. PoW faces ongoing operational and technological challenges to maintain dominance, creating different, but not necessarily weaker, security dynamics. Neither is inherently immune to centralization risks. To claim PoS is always more secure based on a simplistic cost comparison is factually inaccurate.