Why Isn't MLB Under WADA?

Why aren't Major League Baseball or the other US professional sports leagues under the doping policies of the World Anti-Doping Agency, whose work is implemented by the US Anti-Doping Agency which oversees Olympic athletes (among others)?

The answer can be found in a 2004 law review paper by Alan "Bud" Selig and Robert Manfred Jr. (available here):

The IOC and the NCAA are able to ban and test for a wide range of substances, and to quickly add new substances to their prohibited substances lists, because they are not required by law to negotiate such programs with their participating athletes prior to implementation. The athletes are not employees, do not earn wages, and thus are not entitled to be represented for collective bargaining purposes. Professional athletes employed by member clubs of the four major professional sports leagues are entitled to be, and in fact are, so represented. Therefore, the leagues, which all bargain with players' unions as multi-employer associations, must bargain with the players' union before banning substances or requiring testing for substances that are banned. The products of these bilateral negotiations, not surprisingly, have not been nearly as restrictive as those programs unilaterally dictated by the IOC and the NCAA.

 Selig and Manfred explain that collective bargaining has led to weak regimes of doping control:

When regulation of dangerous supplements is left to the collective bargaining process, it is not at all surprising that regulations are not uniform among the four major professional sports leagues, or as comprehensive as those unilaterally imposed by amateur athletic organizations. Players' associations hold different views on the relative importance of protecting players from the dangers of these products as compared to their interest in safeguarding players' privacy rights. In addition, through collective bargaining, parties attempt to achieve gains in certain core areas (such as payroll regulation), often as a tradeoff for, or at the expense of, not making ground in other important areas (such as nutritional supplement regulation). The difficult balancing of these and other interests during collective bargaining negotiations is implicated by drug prohibition and testing, and even more so in the context of prohibiting and testing for products that are legal and can be purchased over the counter.

Perhaps the professional sports should fall under WADA.