As you can see in the links I posted, there is information about accessing services posted on the exterior of the boxes, posted in both Spanish and English.
Yes, it would be possible to put this information anywhere, and in fact, where I live, there are posters elsewhere - in all the libraries, in the municipal offices, at the public pools and other parks and rec facilities, in all the middle and high schools, and there are also posters on buses and trains.
Occasionally there is a news report about a baby - sadly sometimes dead - found in an alley all the same, and the local news always includes the information on contacting social services if you're experiencing a crisis pregnancy, the fact that it's confidential, the law about age limits for leaving a baby in a safe box; this information is available online on multiple news websites as well as the municipal, county, and state websites, in many languages. News reports always exhort the mother to go for a fully confidential medical checkup with no danger of police involvement. From the medical checkup, social services can get involved.
Just because one woman might be unreachable, held against her will, etc, doesn't mean all babies who might be abandoned have mothers in this situation. Many abandoned babies are born to teenage girls who have hidden their pregnancies. The availability of safe places to leave a baby, with information on help that is available posted clearly, offers the mothers the choice of what to do and the reassurance that help is available whenever she is ready or able to seek it.
Even the person responsible for abandoning the latest baby might be able to do so safely if there were boxes available instead of leaving her outdoors. Three full siblings have been found, but we do not know if others have been missed and have perished.
Yes, the mothers need help. But they are a very difficult population to reach. Most of the time the police here will assume the mother is living within a five mile radius of the spot where the baby was discovered, and will conduct inquiries via schools, healthcare facilities and providers, and local organisations.
It is estimated that 4,500 babies have been left in safe haven boxes around the US since they were first installed around the millennium.