A procedure may appear reliable while its most experienced employee is present. The real test begins when another person has to carry it out using the guidance and resources that are meant to be available.
I would examine that handover before treating the procedure as ready to expand across a network. Can a new colleague identify the commitment to the customer? Do they know which choices belong to them and which require someone else? Can they recognise when the task has been completed?
A useful trial follows the work through to its outcome. It records where the colleague hesitates, what information is missing and which exceptions require help. The purpose is to improve the guidance, rather than judge someone for failing to infer an unwritten rule.
The result may call for clearer instructions, training or a decision about responsibility. Those are different needs and should lead to different actions. More documentation will not settle a decision that management has not made.
Consistency becomes more credible when the process can be understood beyond the people who created it. That gives a growing network something practical to share: a commitment, a method and a way to resolve the situations the method does not yet cover.