First look at what leaving predicts. If the next step is a busy street or uncomfortable gear, staying in the crate may make sense to the dog. It can also be a sign they are unwell or sore. Do not pull them out by the collar or tip the crate. Open the door, give space and check whether they move normally when there is no walk to take.
Offer a safe toilet option and notice whether the dog leaves the crate for water, food or a familiar person. If they suddenly refuse to rise, appear weak, limp, cry or miss their usual toilet opportunities, contact your vet promptly. If the pattern is limited to mornings before walks, separate harness or lead practice from the departure. The everyday handling guide can help you make gear practice predictable, but it is not a substitute for checking pain or fear.
A crate should remain a safe place, not a spot where someone reaches in to drag the dog out. Work with a qualified reward-based professional if they guard the crate, growl or panic when you approach. Keep the necessary morning trip short and calm while you work out what part of the routine is difficult.
Today, note what happens after the door opens and what the dog freely chooses when no gear appears. That comparison matters more than a lure that gets them out once.
Sources: Dogs Trust on positive crate use and choice, Dogs Trust on reading fear and stress signs, VCA on recognizing signs of pain.