For many it's difficult to shoot "accurately" using irons sights with both eyes open. But we have to define accurately. For me accuracy means precision and precision has nothing to do with SD/HD shooting. Let's face it, COM at 7-10 yards? A half blind monkey could do that with both eyes open and practice.
Now if you're talking a 2" target at 25 yards it's a whole different ball game. That, for many, is where keeping both eye's open becomes problematic. IME, not many shooters can do that with an iron sighted handgun with both eyes open due to vision issues. If I had to guess I'd say that most of the shooters that say they always shoot a handgun with both eyes open never shoot at a target smaller than a paper plate at close to moderate distances. Some do, but not most. For most it's not possible.
One thing to remember is that HD/SD shooting is not the only use OR the most popular use for handguns. Target shooting, plinkin and hunting are far more popular and everyday uses for handguns. SD/HD types tend to forget this. You want to know the last time I was at a range and saw someone shooting a human silhouette target? Never. So just becasue a SD instructor teachs both eyes open doesn't mean it applies to all shooters. As a matter of fact it doesn't apply to most shooters.
LK