That's not something that would be remotely easy to do and it wouldn't be something that would be fixable for current players.

The game would have to be able to store what outfit you are wearing at the time.

And what about players who were doing story stuff in a silly outfit and forgot to switch to their serious outfit before talking to someone for an MSQ quest and now their cutscene is forever locked to that silly costume. Your solution would mean that they couldn't go back to watch the cutscene in a more appropriate outfit.

What if the player has fantasia'ed to a different race and their outfit at the time was glamoured to be race specific or gender specific and they no longer fit those requirements?

While I'd be fine with them adding this if there was an option to use current outfit, I'd rather the resources be spent on other aspects of the game that would have a greater impact on more players.