Can I add my daughter’s or son’s name to my bank account instead of having a power of attorney?

That is an option which you can do, but again by adding a second party to your bank account, you’re subjecting all of their creditor’s claims to the full amount of the claim against all of the assets in that bank account. The double power of attorney scenario is you are not giving ownership to the agent, being your child, you are just giving them authority to act on your behalf. It’s a much better way to protect the assets for your benefit, and make sure that their creditors do not touch your assets.