PCGS coins are allowed in the US sets because NGC believes that the grading standards are similar enough to be cohesive and on par with the NGC grading. Ultimately it comes down to; their playground, their rules. And it could be worse, 6 or 8 years ago NGC decided to stop allowing PCGS coin in the US sets, a decision that was met with considerable backlash. It has been only a few years since NGC reversed that decision and allowed PCGS coins to again be counted in the registry. Also, in case you were not aware, it is NGC only for the world sets, something that some world collectors would like to see changed too.
You do have a couple of alternatives, you can start your own website and registry designed to suit your needs. Or you could cross your ANACS coins over to NGC (or PCGS) and then use them in the registry here.