I don't think the FairTax recommends anything in regards to how the states raise revenue. It just benefits from the fact that most already have some sort of sales tax collection system in place. I don't think it attempts to influence states in terms of how they collect their own taxes at all.
AFT claims that homeowners will enjoy a ~23% jump in home value. As we have seen from the last few years, more credit, through artificially low interest rates, in the hands of more people has driven property values up, triggering fears of a real estate bubble. This NRST would do quite the same thing. While new construction might drop from ~$200/s.f. to ~$140/s.f., the land prices, which are the only things that appreciate anyway, will fly through the roof.
I enjoyed speculating how the FairTax would effect the housing market, particularly the new construction market. Many of those opposing the FairTax suggested that the fairtax would smother the construction industry because of the increased tax burden... that seems to be the direct opposite effect of what you are pointing out. I think pretty much everyone agreed that there would be an initial increase in value for existing real estate (and used cars as well) but like everything else would eventually find equilibrium. Our discussion was not considering the dynamic you are bringing up... particularly the value of land verses the value of improvements.
I'm not sure I share your favor for property taxes. I recognize they can be used well and have arguably good effects for the community, and I won't argue the dynamics you point out, but I realise that property tax effectively undermines property rights and makes the government effectively the only "owner" of property, and makes all of those who are "legally" owners, effectively renters. I expect I would be vehemently opposed to a federal property tax.
FairTax doesn't go into depth about state revenue, merely mentioning that without the IRS most states wouldn't have much of an income tax system, and they could piggyback onto the FairTax.
I'd be just as vehemenently opposed to a federal property tax. I also agree on the nature of ownership of property v. paying a rental fee (property tax) to the government. It's a moral argument agains taxes on wages and capital. I feel that a similar argument exists for retail transactions, that FairTax wants to collect. You are basically begging permission from the government to be able to engage in a voluntary transaction that is mutually beneficial to both yourself and the other party. It's almost back to the slavery issue with income taxes. One could make the argument that manmade property is different from God-given property. There's also the practical aspect of the fact that we can build more housing units, and more factories, and more 'wealth', but we can't build more land, more sky, etc., and therefore need to conserve it through taxation, and the taxation thereof doesn't decrease it's production.