Rich people spend less of their money and save more of it than poor people, simply because there's more left over after paying for the necessities.
All money is spent eventually. Also, what do you think the bank does with the money people "save"? Banks loan that money to someone else and charge them a higher interest rate than they are paying the savings account. That is how banks make money. So the person who takes the loan will spend it, meaning it will be taxed. When the savings account is cashed out, that too will be spent, plus all the interest earned.
So, in this case, the same money is taxed multiple times. Also, all the money is taxed at the same rate. Currently, loan income is not taxed as income. But under a sales tax, the when the person taking the loan buys new office furniture, it will be taxed.
So, it would be even more regressive than the current system.
Currently, interest income and capital gains are charged a lower rate the standard income. This is how wealthy people pay such a ridiculously low tax rate (Warren Buffet pays less than his secretary). This would not longer be an issue with a sales tax.
Finally, all money is spent eventually. It doesn't matter if it was saved or invested at one point. Even if the person who earned it dies, eventually, all money is spent, even if by his heirs.