If it can't then by its own measure, it's not "scientific". Further, if one scorns anything "unscientific" as valueless, then the principle of falsifiability must also be valueless.

In the relevant sense, yes. We switch out conceptual definitions when they fail to encompass the relevant empirical instances. If falsifiability turned out to allow, for example, theology to be considered a science, then we would have to throw out falsifiability. As it is, it's only a coarse-grained principle for demarcation, hence the arguments about string theory.