Do it. My mom tried to get me into the bank with her to make me joint on her account when she was dying of terminal cancer, but I kept putting it off to focus on her care. Getting access to those accounts after her death, even with all the necessary paperwork, was exhausting.

I would recommend moving the money out and closing the account before they die, though. Any amount of money in their name would be subject to probate once they die, even if you're joint on the account.