The question: are some queens duds.
Answer: YES, absolutely.
For your queen: 3 weeks of nothing is exceptionally ->bad<- unless your climate right now is fall or winter. If where you are it is supposed to be summer, then yes she is not to be tolerated and must be squashed immediately. She may be laying blanks, and the bees removing them as quickly as she laying them. Or she is not laying at all. Both, either, are untenable situations in a summer period.
Sure, sure, yeah, she may be taking a -break-. However, that should be only acceptable to you if the hive is already packed with bees and brood and honey. If that isn?t the situation then off with her head.
Try the feed. It may stimulate. But if she is doing nothing when she should otherwise be working, why fill the trough eh.