Neuronal function depends on the appropriate subcellular distribution of channels, receptors, mRNAs, and other components. Trafficking of subcellular cargo to specific locations is regulated by local signals such as synaptic input, yet it remains unclear how such a decentralized system performs in complex morphologies. We mathematically formalize a popular, conceptual model of microtubule transport (the "sushi-belt model", Doyle and Kiebler, 2011), and show that it can achieve arbitrarily complex spatial distributions of cargo in realistic morphologies. However, we reveal that this model predicts a critical tradeoff between the speed and precision of cargo delivery; given experimental estimates of trafficking kinetics the model predicts delays of many hours for modestly accurate cargo distribution. We explore the possibility that biological mechanisms might have more sophisticated, globally fine-tuned trafficking kinetics to enable both fast and precise transport; however, tuned mechanisms are less flexible, and are fragile to changes in spatial demand for cargo.