Great post there.
So if there is a short in the wire that can burn out the starter and in theory drain battery as well. The fuse is "supposed" to stop this from happening, but I've had a transfer case burn the motor three times before we fixed it, we didn't look for a short until the third transfer case. That was the good thing I chose to let the dealer fix that one, because they had a year warranty on parts and labor, so there was only one charge for three transfer cases. That one cost the dealer a bunch of time and money and parts. So if these two are related, there might be a possible way to this happening as well.
Point being, if you replace starter and there is a short or ground issue, you could burn the starter again and again until you fix short. So if you whack the starter and it works, less likely it is burned out.