Why does audio have standard bit rates whereas video does not
Complexity is the main thing.  Because of how audio works, there tends to not be a whole lot of variation in the quality you get from a given bit rate.  While video often has frames that are very similar from one image to another, audio rarely has the exact same sound playing for a long period of time.

This lack of predictability in audio means that the compression ends up being similarly efficient between one clip and another, so the quality levels can be closely associated to a given bit rate.

Video on the other hand can be predictable or unpredictable.  Some videos sit on the same background for a long time with slow changes between scenes and large areas of similar color within those scenes.  Such videos can be compressed very heavily and maintain their quality since large areas of the same color that remain consistent over time compress very well.  

Other videos may have lots of action on complex background with rapid cuts between shots.  Such video requires a much higher bitrate for the same quality because the rate of change within the video is much higher.

This distinction makes video unsuitable for "standard" bitrates because they are no guarantee of quality.  Instead, standard metrics are based around arbitrary, subjective quality levels of video.  Since there isn't a good concrete way to measure quality level, each company ends up using their own definition of what quality their videos are and use the balance of file size and quality to differentiate their offering.