I think populationist propaganda had less to do with it than hard economic realities. I strongly advocate returning per-child deductions to the real (inflation-adjusted) value they had when the income tax was introduced, instead of treating the decision to have children as essentially equal to the decision to have tropical fish.
How about returning the income tax to the net-net basis on which it was imposed 50 years ago?
I still have my parent's returns for the early 1950's in which they deducted numbers of items that are no longer deductible. The income tax was basically imposed on income over and above the cost of living.
The dramatic expansion of the income tax has been the reduction of deductions, after the steep progressivity was introduced, which originally was justified under the rubric that, well, nobody really needs all that income to live.
Once the high marginal rates were in effect, the Congress went back and reduced deductions, just like they did in 1986 and as they are doing now, effectively, with the Alternative Minimum Tax.