This is the answer. Of the major classic Hollywood studios, only two developed pantheons of mascots that came to represent the entire company - Warner Bros.' Looney Tunes and Universal's Monsters. Disney had Mickey and friends, of course, but Disney wasn't a major studio until much, much later. The other studios - Paramount, RKO, MGM, etc. - had recognizable styles and stars, but not characters who existed separate from specific cast and crew members, whose very image invoked first and foremost the studio itself and not someone they employed (this becomes slightly more muddied with Dracula, who is associated in the popular consciousness with one defining actor, Bela Lugosi. That's why a lot of Universal's current Dracula media and merchandise seems off, since it portrays a generic Dracula who doesn't "feel" right. It's also why Universal tends to downplay Dracula a bit, even though he is one of the top two most recognizable of the monsters, and emphasizes Frank and the Creature - Frank is also heavily identified with an actor, Karloff, but the mountains of famous makeup make the identification much less direct and the creation of a generic Frank much less off-putting.)
Things have changed, of course, and IPs define studios more then ever before. Paramount is Star Trek and Mission: Impossible, Columbia is Spider-Man. But the latter shows just how complex and convoluted the identification between studio and key property can be - even though Spidey is keeping the lights on at Columbia, most people see it as a Marvel and thus a Disney property - which is logical, since they make the films. The Minions are wholly owned by Universal, but they invoke the Illumination subsidiary more then Universal. Only the Monsters, Looney Tunes, and Mickey and friends have the history and clear identification to be fully defined as studio mascots.
And no one has ever cared about Woody. Ever.
