Although I haven't heard the entire Serkin performance, it's certainly a romantic interpretation. I wonder if it was characteristic of the time or if it was only Serkin's conception. In either case, it's a lovely view of the piece.
I may be wrong but I thought that the piano's sonority was enriched by tasteful pedaling. "To pedal in Bach or not to pedal, that's the question," and one not easily answered. Too much, of course, wouldn't be successful, let alone appropriate, and it's quite difficult to do discreetly (if not impossible) at even a moderate tempo without smudging the lines.
You might like to know (if you don't already), that Gould, a pianist I often think of as one who avoided the pedal in Bach, didn't always do so. I can remember seeing videos of his in which the camera clearly shows the dampers moving up and down, something which surprised me greatly (it might have been in the video version of the second Goldberg recording, or in Bruno Monsaingeon's "The Alchemist," or maybe both). Worth thinking about...