Ideally you're correct - but it does have the very large side effect of making real estate fraud much more lucrative. This isn't to say that the potential of people breaking a law means we shouldn't have the law at all - but higher property taxes necessitate a much large spend into property value auditors and require a lot more stringency around property improvement permitting to ensure that increases in property value are captured and recorded accurately.

Except the property taxes aren't based on the actual price paid. The tax assessment and appeal system is more prone to corruption than most states.