50 years ago, we used cloth diapers and diaper pail for the baby. Rinsing them out, first. Same for the grandbabies, except the daughter was using disposables, too.
Far as I know, there is no place doing diapers/pads as separate garbage. At least here, landfills have to be "lined", and they reused the resulting gases for power generation. Considering what else goes in the landfill, diapers must be minor. Some places 'treat" the run-off from the dump.
We're on septic, so nothing like pads can be flushed, and I'll bet that rule is violated in a big city.