Streaming of XML transformations is a challenging task and only a few existing systems support streaming. Research approaches generally define custom fragments of XQuery and XPath that are amenable to streaming, and then design custom algorithms for each fragment. These languages have several shortcomings. Here we take a more principled approach to the problem of streaming XQuery-based transformations. We start with an elegant transducer model for which many static analysis problems are well-understood: the Macro Forest Transducer (MFT). We show that a large fragment of XQuery can be translated into MFTs - indeed, a fragment of XQuery, that can express important features that are missing from other XQuery stream engines, such as GCX: our fragment of XQuery supports XPath predicates and let-statements. We then use an existing streaming engine for MFTs and apply a well-founded set of optimizations from functional programming such as strictness analysis and deforestation. Our prototype achieves time and memory efficiency comparable to the fastest known engine for XQuery streaming, GCX. This is surprising because our engine relies on the OCaml built in garbage collector and does not use any specialized buffer management, while GCX's efficiency is due to clever and explicit buffer management.