Proofreading mechanisms increase specificity in biochemical reactions by allowing for the dissociation of intermediate complexes. These mechanisms disrupt and reset the reaction to undo errors at the cost of increased time of reaction and free energy expenditure. Here, we draw an analogy between proofreading and microtubule growth which share some of the features described above. Our analogy relates the statistics of growth and shrinkage of microtubules in physical space to the cycling of intermediate complexes in the space of chemical states in proofreading mechanisms. Using this analogy, we find a new kinetic regime of proofreading in which an exponential speed-up of the process can be achieved at the cost of a somewhat larger error rate. This regime is analogous to the transition region between two known growth regimes of microtubules (bounded and unbounded) and is sharply defined in the limit of large proofreading networks. We find that this advantageous regime of speed-error tradeoff might be present in proofreading schemes studied earlier in the charging of tRNA by tRNA synthetases, in RecA filament assembly on ssDNA, and in protein synthesis by ribosomes.