Because a common idiom used to "solve" the "class or object method?" question, can lead to odd behavior when a constructor is called as a function and not a method.

I disagree:

How can you disagree with it? Your script proves it. Does not bless {}, ref($class) || $class lead to odd behavior when called as a function (specifically being blessed into main::). Sure it does, and the same goes for bless {}, shift, but that only tells me that both are (maybe) bad, not just bless {}, ref($class) || $class.

To be honest, I am confused by your argument here. You are comparing bless {}, ref($class) || $class with bless {}, shift, saying that they have the same behavior when called as a function and not a method. I agree with that, I have never disagreed. I didn't bring that second idiom up, you did, and in the end, I just see it as having the same problems as the first idiom.

I don't think I ever said that "class or object" is the only possible cause of the odd behavior, it is one of them. And I am not sure why you seem to be implying that bless {}, ref($class) || $class and bless {}, shift are my only (?) two options. I guess I am just not understanding what you are trying to say.

My original point was that practices like bless {}, ref($class) || $class (which includes bless {}, shift) are not really the best since they can create a problem when constructors are called as functions (accidentaly or on purpose).

What leads you to believe otherwise?

I don't believe otherwise, I believe that not checking the specifics of $class is (in some cases) bad no matter how you do/don't it.