While mulching is not absolutely essential for many Australian plants, it does help to reduce evaporation and keep the soil cooler. Mulch also has an aesthetic role in some people's opinion.
Avoid piling on more than 50 mm of mulch, keeping it away from the base of the plant, as excessive mulch can suffocate the soil and is bad for any plant. Always buy good quality mulch from a reputable source so that you can be sure it is not harbouring fungal diseases.
An Australian groundcover is a good, living alternative to conventional mulch if you are willing to be patient while it grows and spreads. Stones and well-placed rocks also act as mulch, and can be beneficial for dry area plants that prefer less humidity around them.