…. with extreme difficulty!
The big toe (hallux) joint of the foot is an very important joint for normal function. When we are walking or running and the heel starts to come off the ground, that big toe joint has to start bending to allow the heel to come of the ground. This is what is needed for normal function. If that joint does not bend that that affects the biomechanics of the foot and can be painful.
Hallux rigidus is a condition in which there is a limitation of motion at the big toe joint and is often painful and is usually associated with osteoarthritis of that big toe joint. Those with hallux rigidus are going to have more difficulty getting the heel of the ground when walking and running because of that limitation of motion and the pain associated with what motion there is that joint.
The higher the heel on the shoe, the more movement that is needed at that big toe joint. So it can be extremely difficult to wear a high heel shoe if you have hallux rigidus due to the limitation of motion at the joint and the pain at the joint. This is the reason why those with hallux rigidus are advised to wear lower heel shoes. Wearing anything over a few centimeters cause the big toe to joint to bend more and can be painful.