Who cares the most about your PM best practices? Who does care the most? Your senior management? They care, but they aren't practicing them and if they've hired good staff then it's likely they don't want to tell you how to do your job, they really just want you to do it and do it well.
Your customer? Yes, your customer likely cares about your best practices. Why? Because they interact with you several times a week on the project and are served...or not served...by your project management best practices. They care.
Your PMO director? Yes, your PMO director cares about your project management best practices. They care about the process the PM's in the organization follow, they care about the consistency of delivery, they care about the customers who are being served with these PM processes and they care about the ongoing success of the projects being led in the PMO. And best practices have a lot to do with that success...at least they should.
Your project team? Yes, your project team will care about your project management best practices – whether they realize it or not. They will be directly affected daily by how you manage your projects, how you manage the team, how you disseminate information to them and the project management processes you expect them to follow throughout the engagement – which are likely part of those PM best practices being conducted and enforced.