Why isn't washing up liquid dry
There's no technical reason why you couldn't make a powdered dishwashing detergent and I suspect that someone probably does sell it, just as there are liquid, tablet, and powdered automatic dishwasher detergents and laundry detergents. It does seem more convenient to use a liquid detergent for washing dishes in the sink. A liquid doesn't need time to dissolve, is easy to dispense without a scoop and if you're only washing a couple of dishes, you can simply squirt a small amount directly on a dish or use one of those brushes with a detergent reservoir.

I haven't seen any dishwashing detergent that had a full ingredients list, but the one I have says "contains anionic surfactants and enzymes". Anionic surfactant typically implies sodium dodecyl sulfate, which is itself a solid, usually found as a powder. The enzymes, while they could be freeze-dried, could retain more activity if stored in solution. Likewise, the fragrances often added to these detergents may be more suited to a liquid form.