It depends on your definition of "appropriate". If you always want the top seed playing the lowest remaining seed, then you are right, that is the most appropriate. This would give you the best chance of a #1 vs. #2 final.
However, if you are the 6 seed who upsets the 3 seed, you might not feel reseeding is appropriate. You would be happy to move on and play the #2 seed vs. being reseeded and having to play the #1 seed.
Do you have examples of amateur tournaments that actually reseed in the middle of the tournament? What's the feedback from those involved (players/coaches) of doing so?
Most tournaments I know from the local high school level up through the college championships leave the brackets as they are and don't reseed.