I think it depends on the nature of the issue. Semi-complex and non-time-sensitive issues like (as an example of something I am dealing with at work with our internal helpdesk right now):
"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.
"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.