Phage therapy is the use of bacterial viruses (phages) to treat bacterial infections, a medical intervention long abandoned in the West but now experiencing a revival. Currently, therapeutic phages are often chosen based on limited criteria, sometimes merely an ability to plate on the pathogenic bacterium. Better treatment might result from an informed choice of phages. Here we consider whether phages used to treat the bacterial infection in a patient may specifically evolve to improve treatment on that patient or benefit subsequent patients. With mathematical and computational models, we explore in vivo evolution for four phage properties expected to influence therapeutic success: generalized phage growth, phage decay rate, excreted enzymes to degrade protective bacterial layers, and growth on resistant bacteria. Within-host phage evolution is strongly aligned with treatment success for phage decay rate but only partially aligned for phage growth rate and growth on resistant bacteria. Excreted enzymes are mostly not selected for treatment success. Even when evolution and treatment success are aligned, evolution may not be rapid enough to keep pace with bacterial evolution for maximum benefit. An informed use of phages is invariably superior to naive reliance on within-host evolution.