If the engineers aren’t oncall, who is? Is it okay to exploit non-engineers? If anything, it is less exploitative to have those who are empowered to improve their situation oncall.
Our support folks handle the on-call support. They do one week each on rotation, they get some extra compensation and the following friday off.
If it's a serious issue they can't handle they might wake up one of us programmers, but usually they can find some temporary fix or workaround until the next morning.