The job of the tax assessor is to provide a value so taxes can be assessed, not to provide real time market data to homenowners. They have limited resources so have worked out systems to provide a fair estimate of value for taxation purposes. These policies differ from one county to another, however they work the same way. In most areas prices do not fluctuate a great deal, so an assessment every couple of years usually makes sense. Plus, when homes are sold, the values are updated.
However, you should know that in MOST cases the assessed value will be either too high or too low, because the market is always changing. And, typically land receives a greater proportion of the value than the improvements.
To your last point, the assessment is fair market value at the time it was performed. In the event of large shifts in the value, the assessor may perform special assesstments to re-value property. In my own County of Los Angeles the assessor re-valued all homes purchased in 2005-2007 because values had shifted so much.
If you want to know how much your home would sell for in this market, as a Realtor.