I think it's because the Led Zeppelin sound is much heavier and less "pop" than the Beatles or the Stones. Even The Who got on the charts with silly ditties like "Squeeze Box."
Zeppelin did release at least one single off each album. Now, Page has been a lot tighter with licensing his music than, say, Pete Townshend, but we have heard Zep songs in ads for Cadillacs and Dior perfume, and in several movies (Argo, American Hustle). The Beatles didn't allow their songs used in ads, and when they did at first, the Beatles didn't have control over the licensing, Sony did (Apple computers, "Revolution"). Even now that Paul and Yoko have more control, they're usually allowing covers of their songs in ads, rather than the original recordings.
Short career? Beatles were even shorter.
Your point about there being little video or interviews to draw from, I think, is valid. But overall I think it comes down to songs being easy to hum with repeating choruses, compared to Zep's long-form songs with long instrumental breaks sung by Plant's otherworldly voice (I mean that as a compliment).
In most US cities, there is at least one and sometimes multiple radio stations that have a daily 'Get The Lead Out' segment where they play three to six Zeppelin songs daily. Some stations have a Beatles segment; I don't know of any that have a Stones segment.
Part of the genius of Led Zeppelin's mystique was the purposeful withholding of access and information about them.
The most blatant example is the fourth album (also their most popular album) where there is not even the name of the band on the album sleeve; and the album had no official name. Prior to the release of The Song Remains The Same (soundtrack), it was very difficult to hear any 'official' live recordings of the band (although some bootlegs like Blueberry Hill were circulating).
The only live recordings I remember was the BBC Paris concert that I recorded off of a radio broadcast. This piqued the curiosity and hunger of fans to experience the band live even more.