We don't read out CMOS sensors in the dark when using them for video, so obviously that's not essential. I'm pretty sure the real answer is that it's cheaper to toss a leaf shutter in than to do it right....
That's where you get the rolling shutter artifacts.
You get rolling shutter artifacts because Canon's CMOS sensors don't have a global electronic shutter. The way a global electronic shutter works is pretty straightforward: in a single parallel operation, you shift the values of every pixel into a buffer. Then, you read the buffered values at your leisure. There's no rolling shutter problem, because the readout occurs simultaneously across all the pixels.
A global electronic shutter is significantly better than a focal plane shutter in every way. Even focal plane shutters exhibit a small amount of roll, whereas a global electronic shutter behaves more like a traditional round leaf shutter outside the focal plane, exposing the entire sensor at once and ending that exposure at once. And unlike either leaf or focal plane shutters, global electronic shutters are almost infinitely fast, so you can stop worrying about flash X-sync speed.
And, of course, they're more reliable....
As readout electronics and speed improve we will eventually get to a global electronic shutter for dSLRs, but we're not there yet.
We should be there. There's no reason you can't do global electronic shutters with CMOS. Several companies have been building CMOS sensors with GES for years. It has nothing to do with speed, and everything to do with simply deciding that the GES is worth the extra sensor fabrication cost and complexity.
Also, as I stated previously, Canon dSLRs do not use leaf shutters.
Sorry, I meant focal plane shutter. Terminology fail.