The problem wasn't so much in the premise but moreso that they didn't have anything beyond that. The animation in the cartoon was so bad that it sometimes was difficult to even tell what was going on -- did that plane just land, or did it crash? The plots made little to no sense and the characters, especially Mandrake, were wildly inconsistent. (To be fair, writers often seem to have great difficulty writing magician characters. More on this in a bit.) The comic was an improvement in terms of both art and writing; however, as it followed the release of the cartoon, I suspect that many people had turned themselves off to the comics without even sampling them based on the cartoon.
The first issue of the comic more or less follows the origin story laid down in the first episode of the cartoon. It varies most widely with regard to recruiting the Phantom, which I suspect was done to get him involved in the story earlier. Although that portion is perhaps the weakest, the comic otherwise is far superior in terms of story structure to the animated version. It makes some changes that make the nonsensical story seen in animated version at least moderately plausible. The stories between the cartoon and the comic diverge there and head off in different directions after their respective first installments.
While series writer Michael Higgins turns in some decent stories, he doesn't seem to handle the group dynamic very well. The third issue is a Phantom solo story, and the fourth is a Mandrake solo story (which reads and looks very much like an issue of Dr. Strange, down to the weird Ditko-inspired interdimensional landscapes). It strikes me that the premise got a little unwieldy before Higgins took it up; not only do we have the four main characters, but each has a son/daughter/protégé, plus there's the "mandatory" cute animal for comedy relief in the alien pet, Zuffy. The son/daughter/protégé angle -- as shown in the cartoon -- seems to be solely for the purpose of highlighting that kids can be heroes, too, as they each seem to take turns providing the deus ex machina du jour right alongside the 'main' heroes. I'm all for the kid being the hero, but it doesn't make sense when they repeatedly upstage their own parents/guardians who are allegedly heroes in the prime of their careers.
But back to the comic, we don't even get to see much of the kids since, as I said, half of the issues are solo stories anyway. I half-wonder if the problem was that the primary characters were too well known as independent entities. The Phantom especially. Even characters like Allan Quatermain did some group work before Moore conscripted them into LoEG. Like I said, DoE seems like a great premise that wasn't very well thought-out.
From what I can piece together, the whole shebang was at least partially brokered by Marvel and/or Stan Lee. I also gather there were a number of legal issues that proved difficult early on, and is probably why we don't see Tarzan in this group. (Prince Valiant does make an appearance in one of the animated episodes, though.) Lee is actually credited with writing the lyrics to the show's theme song -- possibly the worst thing he's ever written -- as well as the first issue of the comic series.
The comic series isn't terrible. Not the sort of thing I'd suggest anyone but Phantom/Flash Gordon/Mandrake completists look for, but it might be worth a read if you stumble across the issues in a quarter bin sometime. The TV show, though, I would highly recommend you stay away from. Seriously, I had to watch the 20-minute opening episode over three separate viewings because I could not sit through the whole thing at once, it was so bad.