... string relational operators all coerce their arguments into string, so that no explicit stringification is needed. But I may miss something.

The OP uses, and Athanasius's reply explicitly assumes, an equality operator, so I don't think you're missing anything. If you are, I'm missing it too, and I'd be very interested to learn what it is.

I agree with you that if you try to use numeric instead of string comparison, you're venturing out onto very thin ice indeed.