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You need a light which has a good CRI. Most LED lights do not have this.
Right now, the LED lights at the forefront of the industry are like the type by CREE still have a pretty awful spectral response. It is not good for color photography.
Xenon flashes like the speedlights have a really good CRI across the whole visual spectrum that comes pretty close to mimicking sunlight.
I have tried to make a decent LED flash (mainly for small size and light weight in this case) but the real problem is relative intensity and the color spectrum.
You can get good intensity with enough LEDs, and driver circuitry can be bought in ready-to-go modules like the type sold by LEDdynamics.
You can use an RGB LED to get a better spectrum, but, the intensity will be limited. Compromises do exist such as LEDs that have both 'white' and RGB on the same chip, but these are just compromises that fall somewhere between the two.
http://www.cree.com/products/pdf/XLampCXA2011.pdf (series of 'white' LEDs)
1st table at the top of page four.
example Red-Green-Blue-White LED
example Amber-Green-Blue LED, see the graph on page 6
I have several LED lights that are used for video lighting 'on the go' where light weight and efficiency (everything runs of battery power -- less efficient - larger battery to carry around) are important. They are unbeatable / unmatched for this application, ie. a 6000-8000 lumen video light that can be easily carried and run off a small battery for 30 minutes at max brightness. But for serious photography, I'm still sticking with speedlights.
Also the overheating thing is a myth. You can probably use it as a flash and not have to worry about it heating up. But a high power setup that's going to be on with any intensity for more than a few seconds will need cooling or it will bake, and that means less light intensity, much shorter life, and possibly burning it up on the spot. Most of the video lights I use have a relatively large heatsink and some have fans, this is an important design consideration, you can't ignore it.