The concept of baby boxes has dramatically reduced the rate of SUIDS (aka SIDS) in Finland and beyond for a couple of reasons:
Affordability: Even in places outside of Finland (where the government does not cover the cost of a baby box), it is a more affordable option than other safe sleeping environments on the market. According the American Academy of Pediatrics (AAP): "Infants should sleep in the same bedroom as their parents – but on a separate surface, such as a crib or bassinet, and never on a couch, armchair or soft surface -- to decrease the risks of sleep-related deaths." The cost of a baby box allows more families to afford this practice.
Portability: The fact that baby boxes are very light, makes it very easy for a parent or guardian to move the baby box from room to room throughout the day and make sure the baby has a safe sleeping environment to snooze in regardless of where the baby might take a nap. For example, it is very easy to bring a baby box into the kitchen while mom or dad is making dinner. Many SIDS deaths are avoidable and are a result of suffocation while in bed with their parents or on a couch or other piece of furniture where there could be extra sheets or pillows causing a suffocation hazard.
Education: Perhaps the most influential reason why baby boxes have reduced SUIDS is due to the extra education that a mother receives which is often part of a non-profit, healthcare, or government organization's baby box program. There are simple safe sleeping habits that many expecting parents are not aware of. Teaching new parents and reminding old parents of simple safe parenting habits can have a very positive effect on the reduction of SUIDS.
Healthcare: It's also worth noting that the original "maternity package" program in Finland requires expecting or adopting parents to seek prenatal government healthcare prior to receiving a baby box.
Temple University has conducted a study of the effectiveness of a baby box program. Long story, short - Temple Study Shows that Baby Boxes, Combined with Personalized Sleep Education, Reduced Rates of a Key Unsafe Infant Sleep Practice during First Week of Infancy.