This is a great idea, but obviously flawed. By simply squaring the total fertility index, countries that produce a lot more than two children per woman get a very high BMI. But they also have a high dependency rate due to that, so they would actually be doing better with a lower total fertility rate.
So a better formula would rank countries of equal wealth with a fertility rate of 2.1 the highest, and countries deviating from that while having the same wealth lower, no matter in which direction they deviate.