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Bandwidth and storage were more constrained.

My take- Photoshop was relatively novel at the time, and motion blur was one of the earliest filters. Do this at varying levels for a few frames and you’ve got yourself an eye-catching animated gif with minimal effort.

Each frame of the GIF in the banners took a noticeable amount of time to load back then, so the motion blur added to the movement effect, as well as signalling to the viewer that it was actually movement and not a static slideshow (which was also a common style of banner animation). I distinctly remember playing with different amounts of motion blur to see which one looked most appropriate for that animation, and simulating acceleration/etc by having the motion blur increase/decrease.