Customer Support is so much more than Service Desk software plus a room of people answering telephones and e-mails. Taking a step back, my personal contention is that a Customer Services team should have a target that the Service Desk is not the customer's preferred "First Point of Contact". A well curated knowledge base is a better option. The catch in that sentence was of course the conditional "well curated": there needs to be a feed-back loop from the service desk to the knowledge base.
I ran a virtual team looking after the Service Desk for ten years. They mostly lived thousands of miles from each other: I had not met more than half of this team face-to-face. Since the service desk had a "follow the sun" mandate, even with a tiny team there was a hierarchy, with a Team Leader to whom I applied the principle "delegate until it's worrying". The teams' mandate was to manually acknowledge all support requests within thirty minutes: none of this "we'll get back to you within four working days" nonsense.