The incentive-compatibility properties of blockchain transaction fee mechanisms have been investigated with *passive* block producers that are motivated purely by the net rewards earned at the consensus layer. This paper introduces a model of *active* block producers that have their own private valuations for blocks (representing, for example, additional value derived from the application layer). The block producer surplus in our model can be interpreted as one of the more common colloquial meanings of the term ``MEV.'' The main results of this paper show that transaction fee mechanism design is fundamentally more difficult with active block producers than with passive ones: with active block producers, no non-trivial or approximately welfare-maximizing transaction fee mechanism can be incentive-compatible for both users and block producers. These results can be interpreted as a mathematical justification for the current interest in augmenting transaction fee mechanisms with additional components such as order flow auctions, block producer competition, trusted hardware, or cryptographic techniques.