Intially, absolutely. As the company grows this needs to be delegated out.
Back in 2008 I used to handle all incoming support and customer service mails. Today, our Support Ninja handles all tickets on Zendesk. Sometimes I feel I should jump back into answering support queries. A part of me says that I have more important things to take care of and getting email notifications for support queries is a huge huge distraction! Besides, a simple faq query need not wait getting answered if I am busy. I should not be the bottleneck. It should be picked up and answered by anyone in the team (this would be my ideal scenario of democratizing the support process).
Support queries can come at any time of the day when you are a SaaS provider. Since I might be doing something more important (UI, Analytics, Marketing, Partnerships etc.) we have decided that any and every ticket is answered by the Ninja. Most of the tickets are generic questions, how-tos, bugs, please give me a discount, billing related queries. These are things that are easily delegated between our Support Ninja and Accounts Genie. Anything outside of this domain gets filtered to me. I have asked them to keep me in the loop with marketing, partnership queries, larger problems, pissed off users and happy customers. Feature requests get put in a master list which I am kept up to date.
Our GetSatisfaction customer forum is very active. I get an email whenever someone posts a new message (or a comment). If its not urgent I tend to reply 2-3 times a week. Others in the team participate if they can get to the post sooner.
As a startup CEO how do you handle customer support?