I imagine it's technically possible but functionally impractical, since image data gets stored in the save file and adding another megabyte or five would make them harder for the game to work with. Also Drake has said that there's a hard limit on how big the overall save data can be for the browser version that he's had to optimize around so that's probably the biggest consideration, and Savin mentions it here too.
It's the same basic idea behind why the game could but doesn't have body-part equivalents to remembering your starting race for pregnancy or 'Hey, like the new look but weren't you a catfolk yesterday?' purposes. Well, that and I doubt any of the writers really want to deal with that much parser soup...
Understood. Thank you for clarification.
I guess this is also the reason Companions do not have full body portraits for all of their "versions" in character window