The author’s analysis is flawed. TFR is considered vastly superior to crude birth rate by sophisticated demographers.
USA still>USSR
TFR is theoretical - actual birth rates are real data. You can estimate a higher TFR than the actual birth rate by assuming a rebound later. The number of babies BORN is harder to manipulate statistically.
You often hear people say they would like to have more children, but they cannot afford it. But people in poorer countries seem to afford large families, even though their real incomes are way lower than ours. Heck, your grandparents (or, for you youngsters, great-grandparents) had 5-7 kids in a family when their incomes, even accounting for inflation, were way lower than ours.
Social security is a big factor. There's a substantial fit, worldwide, between strong SS system = low birthrate, weak SS system = high birthrate. If you foresee that you won't need kids to keep you living decently in your old age, there's little economic incentive to have them. Of course, in the aggregate, we still desperately need those kids anyhow, to pay into this tottery Ponzi-scheme we call a SS system, but nobody thinks much about "the aggregate."
There is a correlation between religiosity and childbearing, too, but --- I am surprised to say this --- not as much as I thought.
What is TFR?