There are several types of property taxes or assessments. The first kind are what are refered to as AD VALOREM, which is latin for "according to value". As it implies ad valorem taxes are based on the assessed value of real estate. So if the house sells the ad valorem tax gets reset. It also can be reset through a re-assessment, either up or down, but the up adjustment is capped by Prop. 13.
Mello Roos, also know as Community Facilities Districts (CFD's) are a fixed assessment. They are typically used to pay for the "backbone" infrastructure in a new subdivision. So if you look at a place like Windemere, before the first house was sold the developers had to spend millions of dollars putting in the streets, storm drains, sewers lines, etc. Since this upfront expense is so large typically developers will create a CFD which is a way to raise capital based on the value of the land, actually, the CFD district sells bonds. When you're paying you'r CFD assessment what you're really paying is the interest on the bond, which is why is doesn't adjust according to the value of the real estate.
The last type of property tax is usually refered to as a parcel tax, again this is not tied to propertyy values, but instead is a set tax. In our area we always have school parcel taxes as well as a mosquito control parcel tax. As their names imply, these taxes are used for specific purposes unlike general property taxes which just go to the county.
Your analysis is correct, if the value of real estate goes down, and the CFD or Mello Roos assessment is relatively high, you can very easily end up with an "Effective" tax rate well over 2%.
As a real world example, there are several masterplanned communities in the Central Valley where the CFD assessment is over $3,000 per year. If the price of a house drops to $150,000, which in some cases it has, then the "effective tax" on that house would be well over 3% per year.
In short this is why many savy buyers will pay more for a home in an area without a CFD or mello roos.
If you ever watch TV sometimes you'll see a commercial for Stone and Youngberg offering "tax exempt" municipal bonds. These are typically CFD bonds and Stone and Youngberg is the bond underwriter. Over the course of the next few years you'll begin to hear in the news about municipal bond defaults, because if enough homeowners in a subdivision don't pay, then their won't be enough money for the bond payment.