If you look at bodybuilding, they have two types of competitions. Natural, and well... the other variety. Personally although the supplement companies are all over the hyoooouge IFBB pro's, who without a doubt have gained a reasonable portion of their mass unnaturally, I think the natural competitions are where you really see the nice physiques.
Some here mentioned earlier that allowing doping would just turn everyone into hulks, but that's ridiculous. I agree that watching huge unnatural hulks run around is nothing but a freak show, just as the pro bodybuilding contests have turned into freak shows decades ago. However the fact remains that in most sports pure bulk is not the key to winning, and beyond that most of the sports where pure bulk can prove an advantage, there are weight classes (think olympic judo, boxing, etc..).
For the non-combat sports, being too big usually slows you down, makes you require more oxygen to operate, and in many cases makes it more difficult to execute correct technique, which has been designed around a more natural body.
Personally I think bringing doping out into the open would do exactly what the scientists think: reduce the risk for both athletes and amateurs dabbling with (currently) illegal performance enhancing drugs. Additionally I would like to point out it's quite plausible that the drugs and methods being used for performance enhancement now because they can't be detected yet by drug tests, are more detrimental to the athletes' health than the "tried and true" ones, such as plain testosterone or other "natural" AAS for example?
Finally I would like to add that while doping should quite possibly be allowed, I would guess having a "natural" class where athletes are limited to more natural performance enhancers, would make a lot of sense, as most people have tremendous respect for those who wish to take their body to the limit without the help of drugs. The important remaining question is whether the fact that an "all-out, doping allowed" class existed would eliminate cheating in the natural class. I would hope so, but human nature has stacked the odds against it.
