Earlier quoted context omitted.
They aren't changing every single tag in the store.
I'd hope not every month! But even if taxes changed yearly is that really a large burden? How many things even stay in the same shelf at the same price for 1 year straight as it is, how many dozens of times was that shelf already restocked and inventoried compared to how often the price tag would need to be replaced due to taxes changing?
Many stores like to pre-tag each product package, either at the store or manufacturer- you couldn't do that if the tax had to be included in the price as the stores have many locations each with different tax rates. (I do think the tax rates should be prominently posted at the door).
Sales tax compliance is already a massive PITA for retail stores. Making them include the sales tax on the tag would just be an even bigger PITA.