The property tax model is a deeply flawed idea because it is subject to a kind of DoS attack. If everybody valued their home at 50% of its FMV, the government would not be able to afford to buy everybody's home. Also, if everybody self-valued at say, 90% it would not be worth the government's hassle to buy everybody's home.

The pie model works because there are only 2 players.

The Greek antiquities thing works because there are probably only a few people that own priceless antiquities and the government is actually motivated to acquire more (because they would prefer they were in museums rather than private hands). So if everybody who owns antiquities self-priced them at 50% FMV, the government would probably be happy to snap them up.

The property tax application would not really work because there are 1-to-many players and the 1 player doesn't really want the item - repossession is only used as a threat/punishment.