No, simply because Bioshock, while being wildly entertaining to many people, was so at the cost of many of the good design choices made in the System Shock games. Just see for example your note about the bright environments and contrast with Bioshock.
(It also irks me a little that your post is missing just enough detail to make it seem as if they made SS2, instead of being co-creators under the lead of Looking Glass.)
I am split whether Bioshock threw away too much or just enough from System Shock 2. At my first playthrough, I was on the edge about this. The "would you kindly" scene cought me as off-guard as the Shodan reveal in SS2, so I forgive Bioshock a lot in the story department. It was definitely the more polished game in many regards.
SS2 is hard to play nowadays and some things (like the ghosts) just really didn't work in hindsight. Also, the crafting and inventory-tetris didn't really add to the game. There is a lot in it that could be removed for good. On the other hand, SS2 stood at a time where those things hadn't been properly tried yet and is a good example of a game that has to be commended for trying out new things. And damn, was it great to actually explore the story.
I heard a (german) podcast about old games a while ago where one of the podcasters said that he thinks that gamers in the 90s had more tolerance for games trying something and failing, because it was such a rapidly evolving medium.
Perhaps, Bioshock was the System Shock for the 2000s and us old-school gamers wanted it to be something that relentlessly tries out things just as in the old times.
Still, Bioshock is light-years ahead in story-telling and world-building than most games of that era. "Would you kindly" is a great example: It shows that the game was built around a narrative and not around a series of set pieces.