There are very few things that are universally true when it comes to business, but I've found this to be one of them:
You cannot build a customer success team, you have to build a customer success organization.
The entire enterprise needs to be behind the customer-centric initiative. This means #CustomerSuccess leaders need to manage a complex cross-functional shift in thinking with sponsorship from the top down.
Customer Success teams that aren't influencing the entire organization to adopt a more customer-centric approach to business end up being a warehouse of customer issues and complaints. Another way to put this, they're playing defense, trying not to loose ground rather than move forward.
A fundamental activity when building a new Customer Success team/program at any company is to go on a road show to communicate what is required from each team AND how they will benefit from this new approach.
"Product Team, by listening to our customers we'll be able to better prioritize our product roadmap to solve real-world problems."
"Support Team, we can reduce a large portion of the preventable problems customers bring to you if we can get your help with onboarding new customers."
In short, clearly communicating what success looks like is just as important with your internal customers as it is with your external customers. It's time consuming and might require some persuasion, but the dividends will pay off long-term.