State Sales Tax Deduction

If I use the table that IRS provides to calculate the deduction the answer comes out way lower than reality. I suspect they do this to minimize the deduction most people take and thus maximize the income tax paid.

 

The alternative that is commonly stated is you have to keep every receipt for every purchase made for the entire year and add up all the sales tax actually paid. I suspect no one does that and thus they use the table which doesn't seem to give them an accurate deduction.

 

If you know the total amount of money you spent last each year, from bank statement for example, you can multiply that by the sales tax percentage and arrive at the amount you actually paid. Will the IRS accept this more accurate approach than using the table they provide?