I hope they do pass such a law, but I doubt it will happen. In the end, legislators have to vote for it and you can bet every church and other organization that would be affected by the law will encourage their members to flood the lawmakers' offices with calls and stage protests. The problem politically is that all of those people have an incentive to strongly oppose the law, whereas Joe taxpayer who would eventually save some tax dollars doesn't have the same incentive to rise up en masse and call for the taxes, or at least nobody will be organizing much advocacy on the other side.
Taxing all property equally is not entirely as foreign to American history as the person quoted in the article suggests, although you have to go back a while. In 1868 the California Supreme Court decided that the legislature could not exempt any private property from taxation, and religions paid taxes on their property from then until 1900. In the 19th Century, at least three Presidents opposed property tax exemption for religions.
It is often difficult to estimate how much taxes are being missed out on because they don't assess exempt properties. But recent studies have suggested the number is approaching $1 billion/year in New York City alone. For all the grousing in this country about excessive governmental budget defecits, it's interesting that these massive tax subsidies almost never even enter the conversation.