LH, the Magdalene institutions were basically about "shame", not about money. More precisely: fighting sexual promiscuity using all means short of murder ("honour killing"). Wealthy relatives were put under considerable social pressure to repudiate the "fallen girl" and to withdraw financial support.

Not only unmarried mothers, but also their children were treated like "bastards", as an additional deterrent for other women.

The reasons for this norm do have a material (financial) component, but are more complex, and deeply rooted in societies based on genetic parentship. (Other models, e.g. avunculate, are successful only in small communities, and have considerable drawbacks as well.)

Fortunately, the power of that deterrence concept has now ceased in most western societies, not necessarily because we have become more merciful, but because we found we need the babies. With DNA tests at hand, the genetic father can be identified and reminded of his responsibility.