Wheel–rail surface damage in curves can be effectively reduced with a lower vehicle Primary Yaw Stiffness (PYS), while lowering PYS is detrimental to ride comfort and vehicle stability. This trade-off can be addressed by integrating hydraulic damping into primary suspension. However, work in this area only concentrated on comparing the effects of specific devices–the full potential of the hydraulic-damping-integrated primary suspension on combating the trade-off considering the whole parameter space is still unknown. Here we address this by making the following two contributions: (1) fully exploring the potential of hydraulic-damping-integrated primary suspension, on minimising the PYS while maintaining ride comfort; (2) systematically investigating the trade-off between the PYS reduction and suspension stroke requirement. Based on a case study using the Mark 4 Coach, this paper found that the optimal hydraulic-damping-integrated suspension can reduce PYS by 97% over the default without worsening comfort. This large reduction can potentially lead to a significant lifetime wheel-rail maintenance cost saving of approximately £42M for the fleet. If a larger suspension stroke is allowed, more cost saving can be achieved. These results provide motivation to conduct detailed engineering design studies to further examine the trade-off between financial benefits and design complexity.