It would be really cool if there were some way to trap the Ender Dragon :P I mean you can bring it to the overworld with the Draconic Portal, but I'd like to be able to keep it as a pet
:P

Have you considered dragon mounts?

I don't want or need to ride it, I have a TARDIS! I want to put it on display in my TARDIS 😁

Dragon mounts would still allow for that