He's not saying that genetics caused the problem, but that natural selection will solve the problem. Natural selection also need not be obviously genetic. For example certain religious groups maintain very healthy fertility rates, while secular populations tend to have quite poor fertility rates. So this logically leads to an outcome very few would intuitively expect - the percent of humanity that is religious will likely increase over the coming decades and centuries.

Also collapsing populations will lead to resource scarcity. One of the many negatives of low fertility is that you end up with far more elderly than working age people. Any given market will also naturally decrease in size, all other things being equal. These factors, amongst others, will completely wreck economies which may well end up creating a vicious cycle against fertility.

Another reason I think 'organized incentives' will be unlikely to achieve much is that Scandinavia had been at the forefront of fertility collapse in Europe and they have both an exremely strong social safety net as well as great minimum maternity benefits. Clearly there are other factors than economic inability driving people to go childless or to only have 1.