Why can't I get this plastic drywall anchor into the hole?
I actually really like those linked triple grip wall anchors (linked by OP). The package often comes with its own drywall drill bit as well. The trick to using them is to pinch the "shoulders" in until they are flush with the sides of the anchor body before pushing them into the hole. Drywall is fairly chalky and brittle, so it will give a little bit where needed to let the shoulders through. Once in, these are nice, strong, low-profile anchors. The auger ones are a lot more destructive and tear up a lot of drywall if they fail. But I've used those successfully in the past as well.