There was a time before disposable, and people figured that out.
First, you empty the load into the hopper. Then you have a diaper pail with a cover to put them in. When the pail is full, you run a load of wash.
Before washing machines there were laundry tubs and a wash board. If you could afford it, you used a hand wringer-roller. There are still people alive who used them.
The air to dry them is free, and a little clothes-line and a box of clothes-pins will do the job. Diapers don't need ironing.
If you're too busy to do it yourself, hire an undocumented alien to wash, cook, make beds, and do the dishes. Your earnings and some of your husband's will cover the cost. /s
This isn’t about me, I’m thinking of how to do all of that in a small apartment with possibly several young kids, not even a welfare mom.
I’m the eldest of five, for us older kids cloth diapers were good, but the younger two who came after a gap were on disposable ones. Very busy mom, one bathroom, no way to tote everything. Disposable diapers were a blessing and she had in house washer and dryer.