Re the comment about American doubles, Jack O'Connor talks about shooting driven birds with a Model 21 in his "Shotgun Book", and being fairly successful. But that's long enough ago that we're not talking extremely high birds--which are a relatively recent phenomenon, given the century and a half or so history of driven shooting.
The shoots I've done have all been in the 200-300 bird range, mixed pheasant and partridge (most of the time favoring the former). If I'm on a peg where I'm not seeing much action, I may take a "low" bird or two that I would pass on if more birds were coming my way. "Low" by the way, must always mean "safe". The blue sky rule: Bird has to be surrounded by sky to make sure you're not going to pepper a beater. But, as noted earlier, you don't want to take too many low birds--even if they are safe and meet the low end of the "sporting" criteria--because you run up the cost of the shoot, which is based on birds bagged (or birds that should be bagged, if whomever runs the shoot feels that the guns are missing a lot of birds that are within their capabilities).
Agree with trw about inexperienced shots at high bird shoots. They're likely to be so frustrated that they won't try it again. And they'll end up paying for the privilege of missing almost everything they shoot at, and essentially subsidizing the bag taken by the skilled high bird shots.
