A project without a process is a ship without a compass

Defined processes become more important when results need to be repeatable (the same person can get the same result) and reliable (different people can get the same result).

The more people must work independently and consistent results are important, the more important it is to do via a prescribed and proven method. On the other hand, if you're going to perform some unique task only once, and there is sufficient communication that people can work together to achieve a shared vision, then allowing flexibility may be preferable. You can start getting results quicker than you can document the process.

I sometimes use a blended approach. We will find something that works initially experimenting as we go, and when we find what does work, we document that process for those who follow after us.

Mark, yes, agree.

Processes with roles and responsibilities provide structure, clarity, and security about the next steps and who is going to do what.

A PMO can support processes and align them organization-wide.

Processes, such as risk management, change management, and scope management, can be defined in a project management plan or an organizational methodology (a PM handbook).