To mulch or not to mulch, that is the question
When giving cultivation information I always recommend local advice. Much is affected by climates and geography, but from afar here are some qualified thoughts.
Mulching generally serves three purposes: To keep the soil cool, to hold in moisture, and to discourage weeds. If your soil is poorly drained and you are in a wet climate you may not wish to mulch. But if your soil drains quickly, mulch could be essentially.
What do we mean by quickly. Generally one can perform a perk test. Dig or bore a hole in the ground, fill it with water and see how long it takes to empty. Sandy soils may drain instantly or in only a minute or so. Silt loams may take 5 minutes and a clay may sit there for hours without a noticeable change in water level. Most people know they have a clay soil because it forms large cracks when it dries out. The usual amendments for both clays and sands are organic matter such as humus. It is always beneficial to add humus, unless of course your soil is solid peat to begin with. If you soil has been amended adequately to provide air spaces in the soil so roots can breath and good drainage, then one can think about the mulch that may be used.
Many gardeners mulch without thinking they are doing so. When one loosens the top layer of soil with a hoe, eradicating weeds, you are also creating a dust mulch. Under dry conditions the change in soil texture of the overlying dust can inhibit evaporation and retain moisture in the soil below. Of course in very dry regions you may also lose you dust in the wind. In semi desert areas it often appears that the soil is gravel because the wind has blown away the finer dust and left a gravel surface. Gravel such as pea gravel can make a very effective mulch and has a couple of advantages. First gravel drains quickly so excess water can soak in or run off, and second molds and soil borne pathogens are inhibited from splashing up on leaves.
When most gardeners are thinking mulch, they picture wood chips, bark or some other organic matter. Dead Iris leaves are organic matter but host the diseases and insects and their eggs that were attacking the iris the previous season. All old Iris debris should be kept removed. That said a mulch of wood chips may be beneficial. I climates like the desert southwest where temperatures soar and the sun is not tempered by humidity in the air Iris rhizomes can be sunburned. They are usually planted everywhere with the top half of the rhizome exposed. But in these types of climates it can be useful to cover the rhizome. The oncocyclus desert Irises naturally grow an inch or so below the surface. In these special climates where the soil surface may exceed 120 degrees a rhizome can be killed. At 112 degrees a beneficial effect of killing resident viruses can occur. But it is a precarious edge to get this effect and not get so hot you kill the plant cells.
In more temperate humid climates the rhizome benefits from some sun exposure and generally it is not wise to cover rhizomes with mulch. But certainly if the season is not terribly wet and the soil drains, mulch around the rhizomes can benefit the roots and inhibit weeds. For most parts of the country it is easiest just to hoe around the clumps and use mulch, if it can be removed when the weather is hot and wet.