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You price it including sales tax. Sticker price is final price.

If someone is buying a banana for resale, or buying with WIC or SNAP benefits (among other things), they would not owe sales tax. So if the price included sales tax, the sticker price would not be the final price.

You do not know the final price until you know how they are paying for it, what they are using it for, and when they are buying it (among other things).

Falsehoods programmers believe about sales tax (among other things).

Then that discount can be deducted by the cash register when it's time to pay.

this is me preempting: yes I know I picked a bad example since produce isn't often taxed. Assume it's a prepackaged organic banana.

$10

This problem is easily solved in countries that use VAT

It really isn't; it's just acceptable to accumulate this rounding error I'm implying in those countries. Which is fine, but should be acknowledged.