Staying in the cage doesn't teach them anything or fix anything.
Many burds protect their cage. My GCC is lighting fast to bite me if I touch her cage when she is inside. Simple fix I open the door and talk to her and have her come out of cage first . Then no bites.
Its seems very easy to have a gcc develop a sudden fear of hands. This has happened a few times over the years I've had Ta-dah. Lots of hand fed treats, rebuild trust going slow and she gets past this quickly.
Lastly nipping GCC is constantly getting threads in the forums...at least monthly, so you can read up and see if there is other tips.
Reading body language is key to not getting bitten. My GCC can threaten to bite many times a week. Usually I just have to pause and give her a few seconds to compose herself and we are back to snuggle and fun, abd I avoided any bites.
Keeping a burd caged is frustrating for everyone and makes things worse. Let them out, set up hands free stuff for them to do. Maybe some very shirt target training. Rebuild bond and trust.
Shift any blames of bites to yourself, if you are getting bites its your fault. If you look at things like that, from that perspective, it much easier to fix the problem. If you need to make observations abd write down when and why.
Baby birds of any species don't tend to bite and put up with us. Adult birds see themselves as individuals and more than willing to correct our behavior. So many people think their burds turn mean at age 1-2.
A good article in general. PAMELA CLARK has many behavior articles that are very helpful
To put it bluntly, keeping companion parrots is similar to trying to pound a square peg into a round hole. The fact that they do as well as they do is testimony more to their adaptability than it is to our husbandry efforts.
lafeber.com