why would you need to have access to prod ?
Your development/staging environment (not local box) should be same as prod in most aspects except capacity so your push to prod is 2 step process developer -> staging -> prod
Developers probably shouldn't have root privilege on production but they need to have read access at the very least. They also should have write and deployment privilege on a few production machines for testing and experiment. Whatever mess they made there should be counted under acceptable loss.
But, I've worked in places that had bad resource planning, and didn't allocate the same kinds of resources in staging. When we had performance problems, there was no place else to go.
It can be hard to convince people to take their expensive hardware and IT time to set that production system up, and now, "duplicate it so we can debug". Eventually, I think you just give up and go somewhere else.