Identifying an efficient and fair allocation of limited donated hearts to patients on the waiting list is one of the top priorities in heart transplantation management. The recent heart allocation rule by the United Network for Organ Sharing (UNOS) has emphasized medical urgency to address the heart transplant crisis by further dividing the previous sickest patient group into three subgroups. However, there is a significant debate on optimality and fairness of this policy because although it can help reduce pre‐transplant mortality, it may reduce post‐transplant survival. We undertake a rigorous study to address this debate by measuring the impacts of a variety of perspectives on the waiting list and patients. We show that the optimal policy of our proposed fluid model is a dynamic priority rule, and provide insight on the impact of fairness constraints on such priorities. We quantify the price that the society pays for following a medical urgency approach, which favors the sickest patients, compared to a utilitarian approach, which seeks to maximize total quality‐adjusted life years (QALYs). Our results, produced by a validated simulation model, reveal that the said price is 7.7% of total QALYs and increases to 11% by considering a broader regional sharing aligned with four‐hour heart cold ischemic time. We study other relevant objectives/measures in transplantation and our results show that the utilitarian policy outperforms the medical urgency policy in other measures as well. Our analysis provides novel insights on optimal patient allocation and sheds light on the debate around this challenging problem.