I only know this from direct experience. Three years as the go-to guy in an understaffed major city public hospital IT department, and it nearly destroyed me, my mental health, my marriage, and my family. In that time there was not one single night that I wasn’t called for something — regardless of on-call status or what my “official” role was. Everyone knew I could fix it, and fix it faster than anyone else. So, I got the call.
In the end, I had to leave. Nothing would stop it. No amount of boundary setting or even being a dick would stop it.
Now I have my own MSP. Customers that don’t get it we fire!
You clearly know what the problem is and how to fix it. Just don’t be surprised when the organization pushes back. They know what the problem is too, and you’re easier than actually dealing with it.