"Bear in mind that the OmniWeb icon "brand" has always been an image of the globe (i.e. Earth) afaik, so to use something else would be quite a sea change (so-to-speak)"
Lets take a look at the progression of the Omni Group corporate logo:
As you see by the above graphics, the initial corporate logo in 1996 is earth mapping centric. However, as you move forward in time, the logo becomes somewhat abstract. Precedence has been set. The Omni Group site itself has pretty good graphics. A abstract OmniWeb logo would solve technical (different image by time zone), geographical (world views), logo similarities (Rosetta Stone language), and be perceived as modern.
The world globe, as a web logo, was rendered obsolete in 1996 when Microsoft IE 3 was released.