Exactly. Companies don’t relocate to save a percent or two on taxes, because the upheaval is something they would rather avoid. It takes a really onerous tax burden to start causing companies to flee on a large scale.
Now, private businesses are a lot smarter about this than the government. They know consumers will switch to competing brands if they raise the prices too steeply, so they are careful to make every price increase small enough that consumers do not notice. Governments are used to acting as if they have no competition, so they have never learned this lesson.
In Massachusetts the income tax rate was dropped a half a percent 10 years ago but you can check a box to pay the higher rate. Less than a thousand do every year.