The assumptions here are wrong because they are based on creating sanitary dishes suitable for human foodstuffs. Recyclables don't need to be sanitary -- just free of large amounts of dirt.

* You don't need rinse water, so the total water needed is at least halved. Since the water is just sitting in a bucket, you can do many, many washings with the same water which increases that efficiency even more.

* You don't need heated water as sanitation and complete cleanliness is unimportant. Heating the water alone uses more energy than everything else put together.

* You don't need particularly clean water, just clean enough to prevent large dirt from adhering. As such you could use floor-cleaning chemicals that clump the dirt and precipitate it to the bottom increasing use time. Reusing water and the chemicals in that water for longer has a very large impact on the environment.

* a couple strokes with a bottle brush take way less energy than a high-pressure pump and once again, get the item clean enough.

* Fewer things going through your dishwasher increases its lifespan and decreases the total cost of operation. This is also better for the environment