Or don't shoot video on a DSLR, use a video camera.
What he said
From Day #1 just about all digital cameras have given users a live video recording facility of one sort or another, basically because it requires little more than a few more software algotithms, which cost little or nothing.
After all, the first digital cameras were little more than domestic video cameras set up to capture individual video frames onto flash memory instead of tape. Although they've evolved enormously since then, the same basic principles still apply, except that capturing tull stills-resolution images at a normal video frame rate is still somewhat beyond the capabilities of consumer-grade battery-powered signal processing. So consequently only a small subset of the pixels is actually used, and so the optical low-pass filter is not optimized for video resolution, and so you get aliasing.
I know the new iPhones are supposed to be able to capture 4K video, but I have a hard time accepting that the microscopic lenses they use could usefully focus that resolution.
Nonetheless, several years ago I made a joking comment here to the effect that "by 2015" stills cameras with 4K video capability would be appearing in Aldi's "Suprise Buys" aisle. Damned if that doesn't look like it might be actually happening!