In the ideal world, a "customer service" agent would perform admirably whether the customer chooses to interact over the phone or through email. This scenario is easier to manage and to staff, and it often contributes to improved efficiencies as agents can be more thoroughly utilized. The reality, however, is that those agents best suited to help customers over the phone aren't always best suited to help agents via email (and vice versa).
One great agent may only type 30 words per minute, making him less effective for email responses. Another great agent may speak with a strong accent, but understands the content perfectly and types 80 words per minute. (Off-shore agents with heavy accents may "turn off" your domestic customer base if put on the phone, but can be excellent reduced-cost solutions for non-voice channels.)
Some agents may have the right skills to handle multiple channels, but simply has a personal preference for one. If you can offer the flexibility to let some agents just handle emails and they actually prefer it, you will have happier agents and (as a result) happier customers.
There's no perfectly right answer for deciding which agents to put on which channels, but be aware some thought needs to be put into the decision. Many agents can and do perform great in multiple channels, but be very aware of those agents better suited for hand-picked channels. With the right agents handling the right channels, you're well on your way to delivering a moment of truth.