Texture Fill Rate = #TMUs x Core Clock
All your TMUs could become useless if they are not feeded with the texels from memory that they need.
Why do you think that we use texture compression ? Because you save 1:4 or 1:8 of the needed bandwidth (& space of course), and your TMUs can reach their maximum theoretical load quicker.
Also, the TMUs have access to a very efficient L1 & L2 cache (fully associative), precisely to save bandwidth.
The problem with the modern games is the heavy use of shading power. But, in older titles, with more simple shading programs, the situation is inverse, and the bandwidth is what matters.
Sucks, because bandwidth isn't growing as fast as the shading power, and we still cannot use SSAA with the older titles.
Hope this helps