Modify your kit to match the environment/weather.
Living in a desert here are the changes I would make to your list (unchanged elements from your list in italics, my changes in bold, my comments in plain font):
Among these are:
A reliable, sturdy knife (I recommend the Chris Cain Survival knife).
A good-quality multi-tool.
A length of Parachute cord.
A definite good start to any EDC list, I always have some para cord, a multi tool and at least 2 sturdy pocket knives with me when I leave the house, a fixed blade hunting knife or an old Canadian fighting knife usually join me when I head out of the urban sprawl along with a walking stick and frequently a surplus British IPK (Individual Protection Kit, a light weight vinyl tarp, about 50 feet of nylon cord, and some aluminum stakes, meant to assist in providing overhead shelter to fighting positions).
A Wide brimmed hat – in addition to keeping you cooler, it can be used as a bag.
As much water as you can reasonably carry and do not ration it, drink when you want to, if you feel thirsty you are already at least partially dehydrated. A common rule of thumb around here is if you can’t remember when you last had to pee, you need to drink more water. – I usually have a 3 liter hydration bladder in the backpack I use for my daily commute to work between the beginning of May and the end of September, that is only 5 miles but you can sweat quite a bit in the 45 minutes it takes from when I walk out the door for the bus stop and when I get to my office door, I frequently use close to 2 liters in that daily round trip when the weather is over 100 deg F.
Learn to construct a simple shade structure, when it is hot out you stay in the shade as much as you can in the daytime, limit your activity as much as possible to night time.
Always carry or wear a bandana. It can be used as a bandage, sling, or carrying bundle. A belt is useful, too. Yes, if you can wet the bandana down a bit it will really help to cool you down when draped over the shoulders, or keep the sun off your neck.
Stay put: You arrive at “lostness” from one direction, a single degree out of 360. If you are in a vehicle that breaks down, stay near the vehicle, it is a lot easier to spot that a person.
Make a base camp: As humans, our sense of well-being is improved when we have a place to call home, even if it is a temporary one.
Locate it in an area that is out of the wind, and where it won’t be flooded during a rainstorm.
This is important even in the desert, flash floods can come from storms you can’t see or hear, stay out of the washes, no mater how much shade is there in them.
Having clothes on is better than being naked, being behind a wall, hedge or tree is better than being exposed to the elements. A light weight long sleeved shirt, long pants and closed toe shoes are preferred. Keep the sun off as much of you as possible and be ready for the temperature to drop a lot at night.
Any shelter is better than none. YES! Shade is good, but remember that all the desert wildlife knows that too, so be careful where you step, sit or put your hands. At least here everything will try to hurt you, if it is not poisonous/venomous it has thorns, spikes, sharp edges, claws or sharp teeth, this applies to the fauna AND the flora.
You main priority in finding shelter is to defend your body from the weather that is it you must keep cool and hydrated to have a chance of survival.
Rob from Mesa Arizona, USA (since I don’t know how far flung the early membership here will be)