Is there such a thing as being a Health Care Advocate for my dad (87) who is coherent?

Download a HIPAA form online and fill it out. Have your parent sign it. Fax to insurance companies as needed.

If you are your dad's caregiver, why aren't you POA?

Whoops, your dad!

Laws are different depending on what state you are in. In my state there is POA for healthcare and a separate POA for finances. Is your mom able to understand the purpose of the POA. If so, she can execute a new one any time she wishes. I have been known to tell companies on the phone that I am my mom to be able to get the information I need to provide her care. Just make sure you have her social security number if you call. Or another option is to have your mom speak to them first and tell them it is ok to talk with you.

POA is usually only for finances, not health care. What you need is a Health Care Proxy which Dad can fill out at the next MD visit and his staff can witness the signature. You keep the original, which you can fax to the health insurance company when they ask for it.
For financial questions, refer the caller to the POA, give them the contact information.