At one time, not that long ago, conservatives were super pragmatic. Far more pragmatic than Democrats. When the conservatives and Republican party were infiltrated by the religious right, which eventually disguised itself and morphed itself into the Tea Party, pragmatism left and the Democrats became the party of pragmatist.
The government benifits immensley from the distribution of birth control. Unwanted births are reduced which correlates to lower welfare costs, medicaid cost, etc. In addition some of it lowers the spread of STD's which lowers medical cost for persons on medicaid.
Strangely, it lowers the abortion rates, yet many from the anti-abortion community object to birth control and/or government involvement in abortion prevention programs such as making free birth control available to low income women.
Pragmatism would be spending a small amount of money to prevent having to spend a huge amount of money. The initial cost of the birth of a child probably covers a lifetime supply of birth control to the mother. The hundreds of thousands of dollars that the government will spend on the child after it is born and until it reachs adulthood is what the tax payer will pay for failing to provide the mom with some free pills or condoms.