According to the article,
Todd Landry, director of Health and Human Services' division of Children and Family Services, said that in nearly every case, the parents who left their children felt overwhelmed and had decided they didn't want to be parents anymore.
In my opinion it is disastrous to let children be dumped like so much not-worthy-of-my-time-to-repair-but-too-good-for-the-trash "Free-cycle" material, especially when states can achieve the same goal by just making it clear that they do not intend to prosecute troubled parents who seek help when they are overwhelmed with child-rearing.
Massachusetts has a "Baby Safe Haven Law" but it only applies to babies 7 days old or less. It is still problematic, though, because it permits the voluntarily-abandoning-parent to do so without providing any information about him/herself or the child. There is then no ability to notify the other parent nor any other family member who might be interested. The babies so abandoned are turned into complete foundlings without any birth-family history, medical history or sense of place in the world that can be difficult to overcome even in the most caring of adoptive homes.
As a society we should be able to help struggling parents and their children without the need to say "Children Wanted - No Question Asked."