Also, notice that most property tax assessments are based on purely physical exterior-visible aspects of a home. If you convert that rats nest of a bathroom into a wondrous home spa, in most places no tax assessment change will follow.
SF is not going to tax your house more because you went from Home Depot subway tile in the bathroom to Murano hand made glass from Italy, whether you file a permit or not. One of my children just had their house electrical system upgraded from knob&tube to contemporary romex, all under a permit, and I don't believe it will have any impact on their property taxes whatsoever.
If you did in fact add a room or enlarge the building, then it's worth more and will/should be taxed more, no? The taxes represent a small additional part of the total cost of the changes, spread out over years.
California Prop 13 causes some serious market distortions.
Thanks