Some states specifically gear their business to exist in certain states due to the Tax policy alone. Generally, a red state will offer businesses more tax breaks and fewer restrictions on employment benefits. This is a huge factor for business since that directly equates to profit. Some industrial based companies will also consider states based on their economic enforcement practices. This as well can equate to profit or loss.
Tax residence is important for companies because it affects their bottom lines and how they make business decisions. When tax laws are changed then the company must spend quite a bit of money to adjust to the new laws. The bigger companies have more funds to deal with these tax laws.
When John Hickenlooper was Mayor of Denver, he worked to raise tax rates on airlines at the airport and companies uprooted and left to avoid the tax rate increases. A company is not a charity and those who confuse the two have no right to be angry when companies move to where the rate of return is workable for them.
I believe tax residence is important for some companies because they have based their decision on how many tax loopholes they can jump through based on that residence. I believe these loopholes should be found and cut off so it's not such an important matter for companies. These strategies involve skipping important tax collections and negatively impact society.
Tax residence is just another thing that companies face to find success. It is a requirement they must abide by and there are consequences if they don't so in that respect is it important but in the grand scheme of business there are many other factors that are much more important to ensure success.