For a company utterly dependent on email, Zendesk came across to me as very naive about email sending.

I did a Zendesk integration shortly after working on a general overhaul of our email at a previous company. The overhaul involved separating out our different types (transactional, marketing, support, etc), and then implementing best practices on deliverability for each of them. Not your day-one email setup, but we were still a small company.

The comparison to Zendesk's approach was astounding. Assuming you don't want to use a Zendesk address (we didn't, customers thought it was dodgy), the email setup they let you do was bad, and their support folks had no idea about any of the details. DKIM, SPF, etc, was all alien to them. Ironically they had pretty bad support in general.