In a doctor-patient dialogue, the primary objective of physicians is to diagnose patients and propose a treatment plan. Medical doctors guide these conversations through targeted questioning to efficiently gather the information required to provide the best possible outcomes for patients. To the best of our knowledge, this is the first work that studies physician intent trajectories in doctor-patient dialogues. We use the `Ambient Clinical Intelligence Benchmark' (Aci-bench) dataset for our study. We collaborate with medical professionals to develop a fine-grained taxonomy of physician intents based on the SOAP framework (Subjective, Objective, Assessment, and Plan). We then conduct a large-scale annotation effort to label over 5000 doctor-patient turns with the help of a large number of medical experts recruited using Prolific, a popular crowd-sourcing platform. This large labeled dataset is an important resource contribution that we use for benchmarking the state-of-the-art generative and encoder models for medical intent classification tasks. Our findings show that our models understand the general structure of medical dialogues with high accuracy, but often fail to identify transitions between SOAP categories. We also report for the first time common trajectories in medical dialogue structures that provide valuable insights for designing `differential diagnosis' systems. Finally, we extensively study the impact of intent filtering for medical dialogue summarization and observe a significant boost in performance. We make the codes and data, including annotation guidelines, publicly available at https://github.com/DATEXIS/medical-intent-classification.