I recently replaced a license plate light bulb. At first I tried to use your instructions on page 10-20 of the Prius NHW-20 manual, but could not make any sense of the instructions. Did you use the instructions for the 2001 - 2003 Prius? All I had to do is remove the tailgate trim panel, rotate the bulb socket (white) counter-clockwise, pull the socket with the bulb out of the lens, replace the bulb, insert socket into lens, and rotate clockwise to stops. For some people it may be easier to detach the electrical connector before removing the socket. To me it seemed like an unnecessary step, because the plug release tab is somewhat difficult to reach.
I agree, it is sometimes easier to replace a bulb without disconnecting the electrical connector. I would do it as you do.
However a less experienced person runs the risk of contaminating the bulb by leaving the socket connected. The wiring may also be stretched/damaged if pulled on too hard.
Actually, my main point was that the instructions are difficult to carry out as printed, and do not appear to pertain to the 2nd gen. Prius. There is no need to remove the backup light lens, for instance. Just remove the socket. Please read the instructions in the manual, and then try to change the bulb as instructed. Didn't work for me, and I have a B.S. degree in Aircraft Maintenance Engineering. Maybe my degree is getting a bit rusty!?