The problem lies in the nature of politicians... Reassessments upset people whose assessments go up, so the big players lobby to defer the re-basing. Or in the case of California, you never revisit until the property changes hands.
In a metrics-based way (#BR, #Baths, square footage)? In an aggregate neighborhood-based way (all 02138 is up 3% this year)? Via drive-by appraisals? Via invasive inside the house appraisals or "broker price opinions"? (The last clause would seem to have significant Fourth Amendment concerns.)
That's exactly how mortgage underwriting works. It's not 100% accurate, but there is an appeals process to address inequities.
This is pretty much the answer. Everyone who argues that it's impossible to figure out a fair value for the property without a change in ownership has to face the fact that lenders do it on demand and (admittedly only theoretically at certain points in recent history) are incentivized to get it right because that's the final method available to them to get their money back if a loan goes south.
2. That process is labor-intensive and therefore expensive. Typically, the borrower is on the hook for the approximately $500-1000 cost of the appraisal. (If you don't see a line item charge, it's safe to assume that was buried in the discount rate.) On the high side of that range, appraisal costs would be > 10% of the tax collected if you appraised annually. Presumably, doing every property in the municipality at one time would make this process more efficient, but it's still a labor intensive and invasive process. The city's largest commercial landlord, Boston Properties, pays about 4% of the total tax revenue in Cambridge. This process could literally siphon more money out of the system than all Boston Properties buildings pay.
Allowing a mandated and periodic governmental inspection of my property to determine its value and funding that appraisal work present significant hurdles to universal application. In this case, I think that approximately wrong is better than precisely correct.
Allow the government to set the rate as they see fit (with all the normal controls of an iterative democratic/representative process), but the assessed value is also a bid of sorts.
Of course there are flaws: an assessment shouldn't vary based on how willing someone is to move, it's still easy to under-assess by a little (but then that drives the rate higher to make the budget), and I'm still a little disquieted by the idea that the control against under-assessing so undermines property rights.
I think that Cambridge (MA) gets this reasonably right. My assessments have tracked the overall market in my area (at least loosely). They might be 10-20% off in a rising market, but they're not 50% off.