Some times they "can't" let go
A truely great Aikidoka will be able to unbalance and throw uke even if he does let go, because they will go with uke's motion. I am not there yet. When I practice I think of why Uke would continue his attack and execute technique based on that "invented" condition. Example: I'm a policeman and carry a gun. If I had my gun drawn and someone seized my wrist in order to disarm me, what could I do? Well, Katatedori Shihonage is a great answer. If he lets go,I'm going get away from him and I might just be justified in shooting him. That is one hell of a reason for Uke to press his attack and focus on my hand/"gun." Next time you do practice Katatedori Shihonage imagine you have a gun in your hand and see where you "muzzle" ends up when you execute your pin. Hee Hee Hee. For you non-gun totters think child, cell phone, wallet etc.
For the truely demented: You are walking through a bar with a cold pint of beer when a team of ninjas attempt to seize your lager. Can you do Katate dori Kokyu Nage without spilling a drop? I say YES!
If you look around you will find Aikido everywhere.