It is well known that having a clear milestone in any project plan would make it easier for the PM and the team member to keep track on the project main tasks and to plan important events, meetings, agreements, and deliverables.
Missing a project milestone would cause a lot of issues in the project process and in meeting the required and attained outcomes on time, which means also ruining the budget plan and so on. This includes missing the project stages start & end dates, missing the critical deliveries, customer needs & stakeholder support. All these issues caused by missing the milestone would hinder PM to follow the right path in the in-process project and the project outcomes.
However, I would agree that some times missing a milestone could be a positive part of a project. For example, missing a due date for submitting a device for the regulatory approval agency. This could be a beneficial extra time for the team to learn about other competitor device issue in which it was unapproved for and to fix it in their project.