Except that you are assuming that assets would be converted into cash and spent on taxable items. If the assets are never sold or are turned over into other investments they would never be subject to the Fair Tax. If the income thrown off is spent on taxable items then that is taxed, but the income is taxed under the current system, too. Under current law, which includes estate taxes, the value of the assets is taxed at date of death (if over exemption amount), and then the income from the assets (if you have any assets left after the estate tax) is taxed, too (except for municipal bonds, of course).
I think to say that the "real" value of an inheritance would be reduced by 23% is an exaggeration. Theoretically, I suppose after 100 years that all of the estate's assets could be converted into cash and spent on taxable items, but with the time value of money I think the estate tax paid now would be much greater versus the Fair Tax paid over the next 100 years. You have a choice whether to pay tax or not, too. Under current estate tax law, you have no such choice.
Most estates are liquidated so that debts can be paid and the remaining assests can be divided amoung the beneficiaries. Most estates are not businesses.