Process matters enormously in customer experience.
Organizations should create standards. Employees should understand what they are empowered to do. Managers should give examples of exceptional service and provide employees with tools and resources to create it.
But there is a limit to what a process can accomplish.
You can teach someone how to follow up.
You can teach someone how to use a CRM.
You can teach someone how to execute a delivery.
It is much harder to teach someone to genuinely care.
It is also difficult to teach work ethic or natural attentiveness.
Those qualities have to become part of the hiring process. Luxury organizations need employees who instinctively notice when someone needs assistance and who actually want to solve the problem.
Give those people a strong process and the authority to make decisions, and exceptional experiences become much easier to create.