People generally earn more after being in the workforce many years. It is no surprise, to me, that older people are having fewer children than young people.
Because I think you are trying to answer the question of whether giving a specific person more money would cause them to have more or fewer children. You want the marginal fertility associated with a given marginal change in wealth. If you don't control for other factors then you are just taking cultural influences (e.g. that possibly some national origins or races prefer larger families) and multiplying them by the association between that race and wealth (e.g. that some race within a given country is systematically impoverished). So, that would be an invalid analysis without the control.
https://www.statista.com/statistics/241530/birth-rate-by-fam...
It shows a clear downward trend in number of births as income rises.