(or "That Grinding Noise? I Think It's Your Protagonists")
Both the Phantom Stranger and Doctor Thirteen, the two characters featured in 'DC Showcase Presents: The Phantom Stranger', have a long history in comics, originally popping up in the 1950s when horror comics were all the rage. Luckily, neither one was too horrific, allowing them to get a new lease on life after the Comics Code killed off EC and the horror boom. They were revived in the 1960s, teamed up in a single comic (but tellingly, the Phantom Stranger got top billing.)
Each character had a good central concept for a storytelling engine. The Phantom Stranger was a mysterious supernatural being, a sort of "wandering angel" who would appear to people in supernatural distress and help them fight it. He had a variety of mystics, demons, and the like as his Rogue's Gallery, and his powers, though vague, were no more ill-defined than Doctor Strange's (one of many "mystic champion" characters who he resembled to some degree.)
Doctor Thirteen, on the other hand, was a far more unique creation; he was a skeptic, a professional debunker of fake ghosts and false supernatural phenomena. Frequently called "the Ghost-breaker," he showed up at mystical mysteries and inevitably revealed them to be hoaxes (to varying degrees of malice.)
Immediately, you see the problem with these two storytelling engines: They can't co-exist. For Doctor Thirteen to be a workable character model, he has to be right; if we, the reader, can clearly see the supernatural at work, he comes across as a stubborn fool and not a expert debunker; and for the Phantom Stranger to exist, magic has to be a real, workable fact of life (since he is, himself, a user of magic.) The two paradigms are diametrically opposed, and that's all there is to it.
For the first few appearances, an uneasy truce existed between the two worldviews. Doctor Thirteen and the Phantom Stranger would team up to fight a seemingly supernatural menace, Doctor Thirteen would be allowed to debunk it in true Scooby-Doo fashion, and the Phantom Stranger would smile, nod...and vanish into thin air. Doctor Thirteen looked smart, but not unshakeably so, and the readers were treated to a "is he or isn't he" mystery.
But it couldn't last. Within a few issues, the series had firmly come down on the side of the supernatural, and every issue consisted of the Phantom Stranger fighting a blatantly supernatural menace in a blatantly supernatural fashion, only to have Doctor Thirteen scoff and say, "It can't be real!" Which is, of course, the perfect paradigm for the Phantom Stranger's series; he lives in a world of mysterious magic forces that use human lives as pawns, and in which larger-than-life cosmic dramas are played out against the tapestry of the human condition. For him, this is the perfect storytelling engine. But Doctor Thirteen's storytelling engine is in danger of being wrecked, because his credibility as a character is getting lost.
By issue #12, they hit upon the obvious solution: Stop teaming them up. Doctor Thirteen gets back-up stories in which he gets true hoaxes to debunk, and the Phantom Stranger no longer has to make him look bad by rubbing his nose in the existence of the supernatural. (And at this point, I'm getting so sick of typing the word "supernatural"...) It's still not perfect; in practical terms, a skeptical character can't exist in the DC universe because the "extraordinary proof" skeptics seek of the paranormal is given on a weekly basis, which makes disbelievers in the...in magic...seem stupid and stubborn. (The exception, of course, being Ted Knight in James Robinson's 'Starman', who perfectly captures the viewpoint of a skeptic in a magical universe.) Doctor Thirteen would work best in his own, out-of-continuity title that didn't have to deal with the baggage of trying to ignore Deadman, Doctor Fate, the Spectre, and the lost kingdom of Atlantis, let alone the Phantom Stranger.
But until then, keeping him away from the creepier corners of the DC universe is better than nothing. And if the Phantom Stranger gets a quiet chuckle at his expense as a result, then let him.