In most of US, the price tag is a legally binding offer, and its presence is required by law in most cases. Here for example is NYC law:

New York City Administrative Code
Title 20: Consumer and Worker Protection
Chapter 5: Unfair Trade Practices
Subchapter 2: Truth-in-Pricing Law
§20-708 Display of total selling price by tag or sign.

All consumer commodities, sold, exposed for sale or offered for sale at retail except those items subject to section 20-708.1 of this code, shall have conspicuously displayed, at the point of exposure or offering for sale, the total selling price exclusive of tax by means of (a) a stamp, tag or label attached to the item or (b) by a sign at the point of display which indicates the item to which the price refers, provided that this information is plainly visible at the point of display for sale of the items so indicated. This section shall not apply to consumer commodities displayed in the window of the seller.

§ 20-708.1 Item pricing.

e. Price accuracy. No retail store shall charge a retail price for any stock keeping item, whether or not exempt under subdivision c of this section, which exceeds the lower of any item, shelf, sale or advertised price of such stock keeping item.

City inspectors may perform random checks to compare tag price to scanner price at checkout and fine store $25-$100 for every incorrect/missing tag, and may repeat the inspections every 24 hours until problem is solved.

If you run around slapping your own discount stickers it wouldn't count since the store didn't do it, you are just committing fraud. The store would be on the hook if it continued to display the fraudulently-mislabeled product for sale after being made aware of it.