>wondering why pci 3 and 4 x16 connections are not typically saturated in games.
Saturating them would bottleneck performance.
Only way to solve the bottleneck would be with a new motherboard, which is expensive, tedious to install, and might be incompatible with some of the user's hardware (see DDR formats) thus requiring further upgrades: overall, a pretty unpleasant option.
On the other hand, it's relatively cheap to make PCI connections that will never saturate under normal use.