Your parent comment described one of the proposed ways for implementing the FairTax system, in which a national sales tax would replace the national income tax.
Even if you did not mean to suggest FairTax and you mean something very different, your proposal still ends up being significantly more complicated than an income tax, since now taxpayers must track all purchases made over the year rather than the relatively limited sources of income they have. Your proposal would increase the compliance burden on buyers, sellers, and the government.
No, my comment said calculate total purchases for the year as (reported income minus reported money added to savings) which specifically does not require tracking any purchases, only income and contributions to bank/investment/retirement accounts and such.
By not tracking purchases individually, and only inferring the total amount of money spent by subtracting savings from income, you can also apply brackets to purchases, and thus avoid the regressive nature of a "simple" flat sales tax.
Even if you did not mean to suggest FairTax and you mean something very different, your proposal still ends up being significantly more complicated than an income tax, since now taxpayers must track all purchases made over the year rather than the relatively limited sources of income they have. Your proposal would increase the compliance burden on buyers, sellers, and the government.