Perhaps someone who has thought about this more can explain how a 'land value tax' differs from existing property tax regimes that explicitly examine the value of improvements and the value of land... This Detroit case is interesting because there are different rates of taxation on the land, but the difference in rate could also be obtained by increasing the land component of a parcel's value.
Land value is therefore a really weird part of the economy that allows people to charge money without doing any work or providing any value in return. If we confiscate all the money people charge to rent or buy land, nothing changes because no work was ever happening. The land is still there and still just as useful. Contrast that with anything where work is actually done - the industry would collapse if you confiscate the money. Taxing land value therefore allows the government to reclaim the money which those people should not be able to charge in the first place (if there was free market competition). When this happens, counter-intuitively, land prices do not rise (because the highest bid in the auction doesn't change) and there is no negative affect on production or jobs (because no one is employed to manufacture or maintain land). We know this because economic theory predicts it and various countries have already tried it. Instead, other taxes can be cut or eliminated due to the enourmous boost in government income, which has very positive effects on the rest of the economy. Understanding how this works is deeply counter-intuitive and so people usually think that a shortage of buildings is driving property/land values because it's easy to make sense of.
To directly answer your question: if you tax the land value as set by the current market, you don't have to worry about assessing other factors that SHOULD lead to higher taxes because the people trying to buy the land have already done that. That's why they are offering a higher price. It's simple and therefore cheap and easy to administer. Also essentially immune to tax dodging because you can't hide the asset.