My thoughts are, to truly achieve success, they do.
It's been done successfully with the Spider. Green Hornet too, though not well. The Phantom SHOULD be easy to update for modern times.
I think that a shared pulp universe with GH, the Shadow, the Spider, the Phantom, Doc Savage, etc. would be awesome. But for that to work, it has to be updated to modern times.
I love the Shadow, but the truth is, how many stories about Nazis, Imperial Japanese and Al Capone-style gangster story lines can you write? They've been written a thousand times already. Period pieces can be great, but nostalgia only carries you so far. Pulp characters are awesome, but to reach the widest audience possible, a book has to be relevant and relevant means stories set in the present. Stories dealing with current events and the world around us, not the world as it was 70 years ago.
DC's First Wave made the mistake of being set in a 'non-time' period. Which almost made it more sci-fi. Not past or present, technology and old stuff mixed together. It didn't work.
But staying in the past has a definite expiration date on it. Why did the Unknown Soldier (admittedly, non-pulp character) go away? Hundreds of issues, but eventually the source material became stale. Too bad they wasted the opportunity with Ennis' mini series. That story should've ended with a new Soldier.
The mood of the pulps is the hardest thing to duplicate, but the use of fictional cities ala DC would make world building that much easier.
And yes, back then the world seemed so much bigger and mysterious, with everything a grand adventure, but there has to be a way to bring that back in the modern world, no?
I just can't help but think that doing proper updates of these characters so that they are relevant with the 'times' and set in a shared universe would be what's needed to truly reinvigorate them, rather than just a temporary wave of nostalgia.
Agree or disagree?