Why does recording a game with Fraps decrease performance?

I can understand that loading new content etc. would slow down while recording, because the HDD is busy writing data

This is exactly what is happening with screen recording software.

You are capturing often up to 30 files of (likely) uncompressed image data every second. 30 large files depending on resolution and color space settings (1366 X 768 = 1,049,088 pixels, 1920 x 1080 = 2,073,600 pixels -- plus the extra 3-4 bits per pixel for color data). This kind of data writing slows everything down, which is why one of the recommendations when screen recording is to capture to a second HDD (not another partition, a second physical disk which doesn't house the OS/program/game).

As far as a second device is concerned, if you could pipe a picture to it and have that second device record the action, then using Fraps as a utility is likely a moot point.