Transistor saturation begins as you drop below a collector to emitter voltage of 0.7V as based on this curve. What you need to remember is that bipolar transistors like this are used as current gain devices, and you aren't really looking at the lower output impedance, but instead the lower beta (current gain) of the device. When you use a transistor as a gain device, you want the change in Ic to be as linear as possible for the change in Ib. In the saturation region, you lose that linear relationship.
In the active region, you get a collector current equal to Ic/Ib which stays fairly constant except for Early voltage effects and you get that linear gain. In the saturation region, the Ic drops significantly for the same Ib. If you are trying to use the transistor as a gain device, you lose a lot of that gain. There are a lot of other effects that also come into play as well that we won't delve into at this time.