You can think of the savings as a perpetuity. The residual value is passed to the next owner if you ever sell.
Think about 2 identical homes, maybe right next door to each other. Both were assessed at $1M. One of the owners fought it down to $950k and saved $362 per year, the other didn't bother.
Both decide to sell one day.
A buyer comes in and he's financing at 3%.
One house is worth $12,000 more than the other to him, all else equal.

Of course things change at the next assessment, but there is a PV to that savings right now.