That sounds like a case for absolutely everyone to undervalue their property unless and until someone wants to buy it (and speculators have little incentive to try to buy houses when nobody actually accepts offers at the low rates implied by their tax valuations)
If no one wants to buy your house at the current value then it is by definition not undervalued. To your second point, speculators can put in any offer they want, it doesn't have to be at or right above your current valuation. If you claim your house is only worth 200k and they offer 500k, suddenly you have a tough choice, either sell, or pay a large tax bill.
If I value my property at a dollar, I'm signalling that I don't want to pay property tax and don't have the slightest interest in selling my property either, ergo there is no reason whatsoever for any speculator to waste their time bidding on it (unless the government becomes a property speculator, or somebody with deep pockets really resents my tax avoidance).
Of course, the system also needs a mechanism to deal with the opposite: nuisance bids from people who don't have the will or ability to actually complete the purchase. Buying property is not like buying shares.
