Having traveled a bit in Northern Africa, I noticed baby sleep problems are virtually non-existent there. They do what humans have done for eons: co-sleeping and breastfeeding. They do it so naturally, mothers are never fully awake while they breastfeed during the night (wife had to sleep in a room full of women and children on several occasions).
Biologically, this makes a lot more sense than giving the signal to the most immaturely born placental mammal that she can't rely on the mother's care.
Denmark sends their kids to nursery school early too and because many women work full time there it means most children aren't with their parent's for a long duration of the day (used ot be much earlier).
What you think about it morally isn't interesting to me. Unless you can prove it's somehow making them worse of then my original position is intact.
Leaving babies to cry or separating them from their mothers for extended periods of time is primarily a health issue which I believe should concern society. [1][2][3] Unfortunately, it fits our economic model very well -- so there is that.
[1] http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.432...
[2] https://www.cambridge.org/core/journals/development-and-psyc...
If you want it to concern society perhaps first you need to make clear what it is you are trying to avoid.
I don't see any evidence which proves some larger societal problem.
However, saying "unless you can prove it" shows ignorance. Not everything is known. Lack of proof does not indicate a hypothesis' invalidity. and I'm not aware of solid proof against it either.