> That't literally the only place where operator overloading makes any sense.

That may be true for C++ (I'll take your word for it), but not for all programming languages in general. For example, in C# it's fairly common to overload == and != to implement value equality for reference types (classes).

Of course, you should really only do this for immutable classes that are mostly just records of plain old data. And C# 9 introduced record classes, which is a more convenient way of defining such classes. But record classes still overload these operators themselves, so you don't have to do it manually.