Maximal Extractable Value (MEV) represents the profit obtainable through transaction ordering manipulation by third parties known as MEV searchers, constituting a significant challenge in blockchains. While numerous techniques have been proposed to mitigate MEV extraction, their effectiveness and practicality remain elusive. In this paper, we address a fundamental question: Is it theoretically impossible to prevent MEV extraction at the protocol layer? We prove that this is indeed the case, making minimal assumptions about the underlying network and consensus protocol, and making no assumptions about MEV mitigation technique. This yields a more general impossibility result than prior work, as it applies broadly across blockchains without assuming specific MEV mitigation techniques, consensus protocols, application semantics, or adversarial thresholds. In light of this impossibility result, we propose shifting from prevention-focused approaches to risk-based deterrents that increase costs and uncertainty for MEV searchers. Finally, we discuss which solution approaches and combinations are likely to be effective and identify areas requiring further research.