Newer/faster standards utilize much higher frequencies in the cable where certain negative characteristics of the cable will have more of an effect, such as NEXT (near end cross talk). Newer cable grades are primarily designed to address these issues.
Other characteristics of the cable standards do not change significantly with higher grade cable and have more of an impact on Examples of such characteristics:
- attenuation/insertion loss - the difference between Cat5e and Class FA (also sometimes referred to as "Cat7A") is only 3.7dB, compared to the difference in NEXT which is almost 35dB.
- propagation delay - (mentioned in Ricky's answer as well) consistent across all cable categories
- return loss - a 2dB difference between Cat5e and the rest of the standards
These latter characteristics have more to do with the limitations of sending low voltage electrical signals on copper wires. As such, they won't ever change much even with other improvements to the cable and these are also the factors that primarily go into determining the "distance" a signal can be sent on a link.
So even with a better grade of cable, that doesn't really have much impact on the distance a signal can be sent reliably on a cable used for networking.