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I was told in the late 70's just the opposite for bleeding brakes, nearest to farthest and have always bled my brakes that way and have never noticed any problems. So my question is how important is the sequence used to bleed the brakes as long as you bleed each line in its entirety?
Not important at all. You'll be fine either way. If you have to do all 4 anyways, why not follow the recommended way ?
The MOST benefit you get is getting rid of the fluid int he calipers. It is in the worst shape compared to the rest. This will always get flushed no matter what wheel you do first.
And to save some time, get as much fluid out of the brake fluid reservoir first, then fill it with fresh fluid before you start. Prevents old fluid from being pushed thru the brake lines.