The reason for having a warning about this is that while undef is a perfectly valid value for a variable, it has no textual representation.

Bullshit.

There are also characters that have no textual representation, and using them doesn't warn.

Note that the warning from the OP isn't even about printing - it's about concatenation. There's a perfectly good reason why most operations warn if one of its operands is undefined, but having no textual representation isn't that reason.