Hmm, maybe a hybrid approach would work. The traditional pinsetter has 10 pins ready to go in a holder that lowers them all down from above. That part seems simple enough. The complex part is creating order out of chaos and loading pins into that holder.
Suppose you keep that holder, and then do this:
(1) After the ball comes through, take note of which pins are standing, then immediately sweep them ALL away into an area back behind.
(2) The holder, which already has 10 pins in it, lowers and releases 1-10 pins as appropriate.
(3) While the bowler is taking their next shot, the robot arm works on picking up pins from the back area and refilling the holder.
This way, the robot arm can work in parallel with the bowler taking their next shot. If the bowler is really fast, the robot might still not be able to keep up, but at least it doesn't have to do all its work super quick in a narrow window of time.