Social Security, Medicare, & Medicaid are payroll taxes. People at or below poverty level don't pay federal income tax, but do pay payroll taxes at the same rate as everyone else. A flat sales tax would be best for the economy, but would be devastating on the poor and thus a non-starter politically. Therefore the FairTax prebates every head of household each month the cost of the tax at the poverty level. Make less than poverty level? You get a net gain each month. Make exactly the poverty level? You pay exactly zero federal taxes - of any sort - because the prebate equals what you spend on the tax. If you manage to save anything, it's tax free. If you die, whatever you leave to your heirs is tax free - you don't have to be a sophisticated multimillionaire with a lawyer to set up trust funds and shelters. The more you earn, the more progressive the tax becomes, but it rapidly becomes quite shallow. This is good because a steeply progressive tax impedes growth by reducing reward without changing risk.
It also rewards responsible behavior. Spend all your income, get taxed on all your income. Save some and you do so tax free.
I also think being taxed on what you spend is completely fair. Why should the federal government have first dibs on my income? The government getting to take its share of my income off the top puts me in the position of being non-free, chattel, with the government as my owner and free to take whatever portion of my income it decides, leaving me to live on the remainder.
As for rich people saving more, I certainly hope so. If I wish to start a business, I'll need to borrow from that money because I don't have enough capital of my own. The alternatives would be to have almost no new businesses (at least only rich people could start them) or to have the government provide the capital. Ever looked at the things government funds? Like the idea of a bureaucrat deciding whether to fund your bakery or your neighbor's floating castle factory?