As Bear said, it's a moist addition to the bedding so not the best if used in larger quantities and in a coop that doesn't need moisture. The bedding needs enough nitrogen to bind with the carbonaceous bedding, so you might not be letting it absorb enough fecal matter to do that.
The question would be, why are you pulling out your litter while it's still at the level that it takes a long time to compost? Most using true DL don't pull out any litter until it's composted enough to use directly on the garden~this they take off the bottom levels and place the top levels back where they found them, which then becomes the bottom levels....has a mulch or soil smell, look and consistency at that point. I don't even pull mine out...it just degrades right back into the soil of the coop and looks pretty much like soil at the final stage. I use a mix of shavings, leaves, pine needles etc but my litter pack never really gets deep as you'd think it should after all the materials I throw in there...it just turns back to soil.
Well the first time I pulled it out because we got mites so I redid the coop. The second time we got lice. So I pulled it out again and started fresh.
So it seems to be about every 8 months I'm pulling it out.
I also like the idea of putting it on my garden so was wanting to put it the compost to speed things up

However you make a good point about the water and moisture. It does flood in heavy rain so that would not be fun. (Which reminds me the third time I pulled it out because it flooded and was under water for a week)