Having 4 kids ages 5 and under, while also running a startup, I can confidently tell you that disposable dishes are the true answer to efficient dishwasher management.
That seems a little strong. We spend like $50/month on paper plates, which are compostable, and I get back many hours of my life that I can use to create valuable experiences with my kids. I don't think that's anymore morally wrong, then say, going on a vacation.
This actually became a political issue in Israel- ultra orthodox Jews could easily have more than 4 kids ages 5 and under while their religion forbids them from washing dishes or use electrical appliances on Shabbat (Friday evening-Saturday) so they tend to buy disposable dishes being in conflict with a country trying to be somewhat green.
Maybe start thinking about the world you leave behind for your kids.