"I need you to disable email address X entirely, and route email address Y to this person, and change distribution list Z to this other config"
Email is perfect for this - I don't care to sit on hold while they click around because it's not time sensitive, and having things written down makes it less likely there will be confusion.
On the flip side, trying to come to a consensus on a nuanced issue or negotiate an outcome with a support person over email stinks, other than the benefit of having it written down. Way better to talk on the phone.
So it just depends on your use case. There's tons of time when I have a simple question and I'd prefer to just be able to drop a line to customer support.
As it is, the phone call convinced me not to use Vodafone. The first thing they did was ask me for my date of birth, as though it's somehow relevant to purchasing broadband. They then went on to ask how much I watched TV IMMEDIATELY after I said "Just to let you know, I understand you offer bundles but I am interested in broadband only - no TV, no phone". When they failed to understand that modem != router I was pretty clear I wouldn't be purchasing service from them.