I'm in total agreement with flasherbynight. It may sound a little extreme, but having immediate access to low and high is really important both for tactical use and EDC use. I'm not saying that all my lights have that functionality, but all the ones that I have in my EDC rotation do.
As you've pointed out, it is really hard - if not impossible - to meet every criteria that you need in a single light (which is why none of us own one flashlight, right?) but flashlight design has gotten so advanced now that you can get most of the things you need out of one or two lights.
For me, an EDC is not something to take lightly. It's a tool, like any of the others that I carry and work with every day. I'm an engineer and many of you will appreciate that an engineer, like a mechanic or a tradesman cannot do a job properly without the correct tools and more importantly, tools that are made to a high standard and are reliable. That brings me to my first necessity for an EDC,
reliability. I need to know that when I need it to, it will do its job.
The others are less important but still matter. I clip all my EDCs except my 1xAAA backup to the pocket on my jeans, so they have a strong pocket type (not belt type) clip. I also like the light to ride low in my pocket and simply for asethetic purposes, the clip to be something more than a strip of metal i.e. have a design.
Runtime is obviously important. On low, I'd need more than 5 hours and on high, at least 60 minutes. This often dictates battery type as well, and recently I've favoured 1x123 lights over anything else for EDC. That's obviously what this class of light was designed for. Tactical modes are less important on EDCs than lights I use for more specialist purposes, so as long as the light has high and low and maybe the option of adjustable levels, I'm happy. Even though I own both, clickies have always appealed to me more than twistys, but again this is something I'd be willing to compromise on. My often carried RA Twisty and Bitz lights are prime examples! Last but not least are ergonomics and asthetics. A light is nothing if it can't be used easily and properly and let's face it, we are all suckers for a pretty flashlight