GPRs and AEGDs are postdoctoral programs for people who want to be general practitioners but rather learn more about practice in an educational environment as opposed to a commercial practice. A GPR/AEGD should give you a better clinical understanding that you can carry over to working in a practice.
Once you pass your boards, you shouldn't need to practice under any dentist. However, opening up a new practice is very expensive and depending on the saturation of the area you decide to open the practice, you may have trouble attracting patients. These two reasons are why many people decide to do an associateship after graduating.
So even with a GPR/AEGD, you'll still run into the same problems with starting a practice from scratch, though you might look more attractive to someone looking for a good associate.