In my opinion, phone support is frequently requested but hardly ever needed. I worked at Twilio and as part of my role as a Developer Evangelist I responded to help desk tickets part of the week. We didn't do any phone support and we were able to help people effectively.
The key is to be very detailed, thorough and courteous in all your correspondence and also to ask for clarification if you don't understand their questions. You should also have a library of online resources like documentation, frequently asked questions and forums that you can refer people to so they can easily find answers for themselves once you point them in the right direction.
One caveat to all that though: I worked at another company that provided phone support but it was something you had to schedule and pay for in advance. At first, I thought it was crazy but our phone support people were busy all day helping customers. It wasn't a lot and it didn't even cover our costs but it prevented your phone from ringing off the hook and people calling to ask really stupid questions.
Hope that helps! Also, if you're looking for technical advice on setting up phone support options I'd be glad to help you... over the phone! :)
Offering easy and quick access to your support team is one of the best ways to delight your customers. Even if they have a question that can be answered via email, being on the phone with them gives you the opportunity to calm down a frustrated customer, provide solutions faster, and present a positive image of your business by being friendly, personal, and helpful. On top of that, as in marketing and sales, it's important to be present wherever (and however) they're looking for you, and if they're searching for a phone number on your website, only to find that you can't be contacted by phone, you're likely setting them up for an even more negative experience than the one they were already facing.
I would suggest looking at it from the perspective on what type of phone support is required in general depending on complexity of application and real-time access to information. For example, if the service is a SaaS based contact-centre solution, then you may need phone support for customer confidence/loyalty if they are worried about access or loss of data in real-time. If the service is more of an office productivity tool, then as the previous experts listed you need to look at the alternatives prior to someone having to pick up the phone (i.e. FAQs, manuals, discussion boards, on-line forms for various types of requests/feedback or even a LiveChat window).
