Regarding the series concept, the biggest advantage is that it allowed an easy way to introduce a new world.
If non of the characters came from this world, the world building is easier, and the viewers learn about the world along with the characters.
(This was kind of wasted on the old show, that didn't have much of a world building anyway)

However, this isn't required, and there are better way to introduce a world by adventuring in it and slowly bringing more and more elements on the surface.
"One Piece" is an example of how to do that well, but it certainly isn't the only one.

The biggest problem I had with the old series, is that the adventures felt forced and unnecessary.
The group didn't go for adventures because they were needed or felt it was the right thing to do, it was more because some wacky DM told them to do so.
That kind of cheapens what they did every episode.