The challenge of making healthcare decisions for incapacitated patients continues to confront stakeholders worldwide. Annette Rid and David Wendler proposed a Patient Preference Predictor (P3) that uses population-level data to infer an incapacitated patient's likely treatment choices, with the aim of aligning care with the values and preferences they held when last autonomous. Some objectors claimed this would fail to respect patients' (former) autonomy because the basis for prediction would not be specific to the individual (e.g., based on data reflecting their own specific reasons for preferring one course of action over another). In response, we proposed a 'Personalised Patient Preference Predictor' (P4) that would harness the predictive capacities of personalised large language models (LLMs) fine-tuned on individual-level data of various kinds. The envisioned P4, if realized, would be akin to a 'digital psychological twin' or AI simulation of the patient that would encode their unique preferences and values to enable an individualised prediction of their likely treatment preferences. The P4, in turn, has been criticised on various grounds: philosophical, practical, and ethical. Here, we comprehensively evaluate the concerns of our critics based on all known published critiques as of the time of writing. While acknowledging the weight of some of these concerns, we argue that they do not entail that a P4 should not be developed. Rather, the concerns point to areas where thoughtful design choices, responsible regulation, and further philosophical reflection are needed to steer the proposal in a positive direction.