Ask HN: Turning a Sysadmin/Support Team into a DevOps/Project Team?

I've noticed that some DevOps teams struggle with project-oriented concepts, and my theory is that these teams are made up of people whose experience has been in support and systems administration rather than software engineering.

I don't mean to dismiss or insult the support/sysadmin career path or experience, especially since I started out on that track! I've been lucky in that most of my career I've worked closely with developers, R&D, and academia. That has given me exposure to project work concepts such as requirements, acceptance criteria, sprints, etc.

My progression from sysadmin to DevOps took place over more than a decade; how do I help people who haven't had that gradual change embrace the more software development style mindset? One team I am working with is very focused on support tickets and interrupts, and I'd like to help that team switch to a more project-based mindset.

How do I help people whose background is in interrupt-driven work change to working in sprints with requirements, features, etc?

Or do you disagree with my fundamental assumption that people whose experience has been in support have a harder time moving to a project-based workflow?