Why isn't the LEGO logo on studs in more official computer animated shows, movies, and games?
I can not give a clear answer for licencing, as that is a very broad topic covering various mediums and possibly covers legislation across nations and regions. There are a few practical design cases I can think of though.
Early media
For interactive media, games historically have had limitations on processing and graphical power. Early games, such as LEGO Island released in 1997 had extremely limited graphics (by modern standards) yet were still very effective at representing LEGO bricks and characters fully.

Rather than attempting to recreate LEGO pieces as realistically as possible, they aimed to make the characters and environment full of life, immersive and fun. Very important for a product aimed at children.
Many designers completely ignore the realistic limitations of the hard plastic joints and pivots of a real minifigure and went for a more expressive style. Arms and legs unnaturally contort to give more expression and dynamics to the characters.

I believe the idea of LEGO bricks and what they represent to the imagination were considered more important to the physical aspects. Aside from technical limitations, the need to represent the bricks as accurately as possible just was not necessary and could even detract from the style.
It is even possible that rendering every individual stud on a brick could have produced a sickening Moiré effect as objects were moved around and their scale changed. This issue would be particularly worse at lower rendering resolutions.
Hyperrealism
The LEGO Movie released in 2014 was perhaps the first time LEGO fully embraced realistic animation. Although being fully animated digitally, they embraced the visual aesthetic of fans making stop-motion LEGO animations (also known as Brickfilms).
The painstaking details, involved placing minifigures under microscopes to capture the seam lines, dirt and grime into the digital textures. The character Benny the spaceman for example, includes the broken helmet chin strap, a common defect of the space sets.

It seemed from the design brief, it was important to provide realism to capture the physical nature of bricks for the sake of nostalgia, in combination with having certain creative freedoms to still make the parts feel alive and animated.

Summary
I could quite easily cover many more examples but I think it would generally be the case that many production companies contracted to design these media by The LEGO Group would have their own production standards, guidelines and interpretations of the artistic and technical style.