I have twelve dinner plates. Often I'll use two a day (my partner doesn't share my allergies or diet and mostly uses bowls)

We have many hot drink mugs

We have twelve sets of cutlery

The dishwasher runs when we run out of clean [plates|cups|cutlery] that is weekly or less often

Modern dishwashers can easily clean tons of crust. That's why it takes them so long. As long as bigger chunks are gone and you clean the trap you are fine.