Only if you ignore estate taxes...which FairTax eliminates.
For the rich (defined here as anyone with enough wealth that, if they don't spend it down, they will face estate taxes) they either have to realize the gains (and be taxed) and spend down or leave an estate which will be subject to estate taxes, giving them a maximum time window on taxation equal to their lifespan.
With "FairTax", which eliminates estate tax and goes to a strict consumption tax, there is no such maximum window.
> And consumption taxes benefit debtors at the expense of creditors. Income tax makes the debtor pay back the debt with after-tax dollars. Consumption tax causes the creditor to be paid in pre-tax dollars.
Because it also changes the cost structures on which debt is occurred, this only is meaningful as a one-time effect on debts that exist at the time of the transition to a predominantly-consumption-tax system, not as durable feature.