Without a doubt, Customer satisfaction would rank up higher than all other goals for a support team. Often, the customers need a simple nudge to remind them about the satisfaction survey or NPS, whichever helps in measuring your customers' delight.
How do you structure your followup email sent after the agent resolves the customer's issue? If you think you've got the flair for best lines, why don't you share the secret sauce with the community?
Just leaving here a standard template that merely nudges the customer to fill the survey.
"We’d appreciate your feedback you have to offer about your experience with support. Please fill the survey attached to this mail to let us know how we did."