IOW, we're still looking for a use case that warrants removing the identity-implies-equality guarantee out of Py_RichCompareBool().
I can think of two use cases: 1) IEEE-like behavior. Before you say that there is nothing wrong with making floating-point comparison yield true for NaN==NaN, let me remind you of the beast called "Signaling NaN", which should raise an exception on any operation, including comparison. 2) A class might have comparison operations that put trace information in a log file for testing purposes. Such a class might be intended to help in testing searching algorithms, for example. I think it would be useful to be able to know whether x[i] is ever compared with x[i] by putting appropriate tracing comparison operations in the elements of x.