That is a wise plan and it is exactly how it works. Every country charges exactly the highest tax they can charge without driving business away. But the tax rate is not the only thing the business has to consider. They have to consider stuff like labor costs, established case law, cost of regulatory compliance, likelihood of civil unrest, corruption, etc. If a country creates conditions are good for business then a country may be able to charge a higher tax without driving business away.

Let’s accept your premise. Every country competes to provide the best business environment except one. One country doesn’t compete, on principal, because the result will be that “everyone suffers”. Now who suffers?