The Batman doesn't want to bring in a sorcerer like Dr. Fate to keep the whole thing (somewhat inexplicably) secret. But then he brings in (or lets B'wana Beast bring in)...the Crimson Avenger? To go door-to-door looking for a pig? Other then as a cheap sight gag, it doesn't really make much sense to bring in the Crimson Avenger but exclude Dr. Fate, who might be able to actually do something to restore Wonder Woman or find her in pig form much more quickly via magic.