I keep a 2" +/- thick layer of straw in all the rabbit hutches in my rabbitry of 22 does and 3 bucks. It serves a few purposes for me. The main reason I do it is to have a constant supply of rabbit manure infused straw to use as a mulch in my fields. Piled on thick, the straw is an effective weed suppressant that will break down in time to become soil, it also attracts worms and supports mycorrhizae development. The rabbit manure, urine and hair that is infused in the straw provides all the fertilization that the plants and trees need for the most part, you can read about that here.
Worms tunneling around in the soil aerate it which increases the amount of water that can get into the soil as well as improve drainage. They feed on plant debris like dead roots, leaves, grasses, and leave behind their nutrient rich castings which are packed with minerals such as concentrated nitrates, phosphorus, magnesium, potassium and calcium that help with the plants growth. Earthworms indicate a healthy life in the soil and seeing them wiggle around in the soil when we're planting is always a happy thing! Attracting worms into any garden bed or field is just good sense.
Mycorrhizae is a fungus that grows in association with the roots of a plant in a symbiotic relationship. The fungi colonizes the root system of the plant and spreads throughout the soil. It's magic is that it'll grab nutrients and water that are out of the roots reach and channel those nutrients back to the root of the plant. In return the plant provides the fungus with carbohydrates formed from photosynthesis. Mycorrhizae also helps to increase the plants tolerance to different environmental stresses, and they LOVE straw. Deep mulching with straw is a great way to get the fungi life active in garden beds and fields.
As far of how it benefits the rabbits, I have found that having a thick layer of straw in the hutches means I don't need nest boxes for the rabbits to kindle into. The rabbits build their nest anywhere they want to in the hutch with the straw that's already there. They kindle into their nests without fail, every time. If young kits get dragged out of the nest by mistake, they don't die on the wire as there isn't any exposed wire. I have often found kits in the morning that are outside the nest and cold, but not dead. I can warm them up quickly and get them back in the nest with their litter mates. I also have several does that will build a whole new nest with the straw that's in the hutch around a stray kit, keeping it warm until I can put it back in the proper nest. It's not that I never lose kits to the cold, it does happen from time to time depending on the weather, but it's very infrequent.
I do have to clean the rabbit hutches every few days, but it's not difficult or even time consuming. Rabbits create an area in their hutch which they always use for relieving themselves, much like cats using a litter box that's always in the same place. It's always in a corner they chose, and to clean it I just have to remove the manure infused straw from that corner, move some of the clean straw that is already in the hutch over to the corner I cleaned, and add some fresh straw to hutch to bring the straw layer back up to normal. In doing the 'cleaning and replacing straw' maintenance every couple of days, I end up with a couple of large piles of manure infused straw every month to use in my fields, row crop, garden beds and around the base of fruit trees, you can read more about that here.
To make the 'cleaning and replacing straw' job easier, I build hutches to accommodate the task. All my hutches are wood framed and individually free standing (for the ease of making any repairs to them that may come up) have large doors that swing open on side hinges with lots of upper body space for my ease of getting into the back corners for cleaning them, and are all 2' off the ground so I can toss the manure infused straw under each hutch with every cleaning, where it stays until I either use it, or pile it elsewhere for future use.
The piles under the hutch grow quickly during breeding and kindling seasons. The does eat more food when they're pregnant and nursing so they produce more manure. Then the kits start to grow and eat a ton of foraged foods and hay and they really add the growing manure piles. When kindling season is over, and the last grow outs have been butchered in early summer, the manure production slows way down. In the hot summer months the rabbits aren't as hungry, they don't eat much and don't produce much manure, cleaning the hutches can be done once a week or less, depending on the rabbit.
In the our triple digit heat, the rabbits don't like their hutches being full of straw, it cuts down on the air circulation that helps to cool them off. Even if I put a good layer of straw in the hutches, they'll move it all to one side so half or more of the cages floor is exposed, and the large pile of straw they moved to one side becomes a cooling shelter from the heat, and they'll bury themselves in it during the hottest part of the day. Once they've moved the straw into a pile, the floor is now exposed and the urine and manure fall under the hutches without building up in the straw. A few of the rabbits seem to like to have a straw layer for their manure, and keep that corner of the hutch full of straw even though they've cleared the straw away from most of the floor space. Still, it doesn't collect manure quickly as the rabbits don't eat much because of the heat, and they aren't producing much waste.