By the time I left my last position, I was hardly doing any heads-down work. The team was an internal platform team, and the leadership was actively against sourcing any feedback from the eng/data teams we were meant to serve. The only things that were ever on the roadmap was long-term refactors that no one was asking for. My feedback on the direction of the work was by-and-large ignored, despite the fact that I was the only person writing any code on my project.
I started a new job and it's been a night-and-day different. Furthermore, the lead engineer of the project is a grinder which motivates me to at least pull my own weight.
TL;DR if you're an eng manager and want your team to be engaged, then lead by example, give them tangible goals, and listen to what they have to say.