I had 3 high torque hitec digital servos for a robotic gripper design application. These were rated at 7.2V with stall current of 2.9A. Since I was planning to use all three to work concurrently, I used a B&K precision digital power supply with 7.2 V and 6A capability to power all three of them. While testing, two of the motors stopped working and when contacted hitec support, they said they were burned out. They said since I was using 6A supply and using 3 motors in parallel, each of them was getting around 2A, and that was too high for the servo.
That was a major learning experience, but now I am confused as to what would be the ideal power supply ratings i should use. I still need to operate the 3 servos in parallel because they actuate three fingers sof the gripper, and are under a high load when grasping.
The problem is not the "current", it is the "HEAT" generated by the current in the motors that killed the motors. You need to design your project using servos rated for CONTINUOUS holding torque and use heat sink mounting to dissipate that heat.
Your power supply has no bearing on your problem. You MUST have a design that reduces the current to the servos to the bare minimum once the object has been gripped and the servos have stopped moving. How you would do that, I don't know.