That'd be much too slow, and much too much work to change the animations for such a major thing just for one class. I'd much prefer their time be spent elsewhere.
Actually, in the past they have used similar animations for all PC races because it was easier to just recycle animations than hand make animations. With Havok Behavior, it takes a lot less time and effort to create animations. It could be done if swimming like that is the way they want it to be. From the way Bethesda talks, each race is distinct in every way, which means they all have a unique look (which we know not to be just an exaggeration now from what we have seen) and probably highly unique animations to differentiate them as well.