As I understand it, the prerendered backgrounds in these games were rendered as video clips. This was an efficient way to superimpose 3D on a 2D backdrop. But I imagine it may have affected how crisp the backgrounds could look.
Use of video clips for backgrounds was possible but rare. The opening of Final Fantasy VII is a good example, where it blends seamlessly from the opening FMV to control of the characters. You are correct that it affected the quality. You could easily see the video compression artifacts. The more common non-video backgrounds looked better.
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