Here's a good place to start: Set Users’ Site Roles
Site Administrators can do pretty much on a server and it allows unrestricted access to the configuration, all sites, all users, all projects, all data, all workbooks, etc. In other words, they have full access to everything (for the given site). It's incredibly dangerous to have that many people as site admins as eventually someone will break something. Site admin really should be reserved for only the people who are actively administering the Tableau Server. If these developers just need to publish dashboards, then the Publisher role would probably suffice.
This is what I have been trying to tell them- however it doesn't seem to be sinking in. They think if someone is a developer they should be able to handle Admin responsibilities as well.
I'm going to have to find some real world examples that I can apply to our department to show them- what can happen, worst case scenario.
Yikes! I think some real world examples would be a good next step. Keep fighting the good fight. I hope that you break through before someone makes a huge mistake.
I'm hoping that will scare them into realizing that there is a reason we have Admins.
As you both are aware, I'm sure it's hard to convince them until they have experienced something like this in the past. It is very easy to overtrust- until the mistake happens.