but we don't have to pay the FAA a fee to keep our private pilot license/certificate.
Not quite true if the new regs come into effect.!
The FAA are finally going to implement the photo id cert which will require a new photo every so many years and the FAA have stated an intention to implement fees going forward.
Various $ figures have been mention with $50 for the issue and $25 for a replacement etc. (currently the FAA charge a nominal $2 for a replacement cert).