No, my reasoning is the same as the Church’s:
See Vatican link above. Our obligation to the children is not contingent on their origin. We Catholics do not put life on par with material goods. It is an absolute and unabridable right. Similiar, we do not put conditions on our Christian obligation to the less fortunate. Our call is not to judge others, but to be in the service of the weakest among us (regardless of our own impression of their spiritual state).
The concepts you are professing, that human life is like possessions and obligations to the weak with regards to their continued existance only goes as far as is completely-convenient-and-of-no-cost-to-oneself, does not really match Catholic “right to life” principles (see GENTIUM LUMEN and CHRISTIFIDELES LAICI).
We believe that God values each life infinitely, that is why abortion and euthanasia are absolutes and why the Church so forcefully objects to modern applications of the death penalty. And we are to love our neighbors as ourselves (generally as close to infinite love as we can come). It is easy to claim to love fetal life and unwanted children, but an unwillingness to go beyond no cost efforts would seem to profess that, in reality, we love our own lifestyle and things more.
This is another of the seeming contradictions between different aspects of “right” thinking. Concepts like “mine”, “earned”, and “deserved” are very popular, but at odds with Holy Scripture.