You can't store the wet clothes in the washing machine until you want to use them again. You have to dry them and iron them (or at least shake out the creases and hang them) first. The main point of the two dishwasher trend is that you can just use the clean plates straight from the dishwasher without bothering to put them away.
You don't wear the same set of clothing every 1-2 days like you do with dishes. You also don't tend to wash your entire wardrobe in one go.
You are always wearing or using some kind of textiles at all times, unlike crockery, which you use at set times and ignore the rest of the time.
Plates dry almost immediately during the dishwasher cycle whereas even a washing machine with a drier doesn't get clothes usably dry in a short amount of time.
Washing machines don't spread clothes out in nice attractive rows, you'd have to lean into a horrible rubbery damp steamy small space to select the clothing you wanted.