All this talk about Willie Nelson's guitar got me thinking about what's under the skin.
Mervyn Davis once said to me that the saddle is the interface between two systems. The first being the strings suspended between nut and tailpiece or bridge. The second being the bridge itself (which many makers regard as a brace) and the under the top bracing.
With that in mind here's a "skeleton" of a steel string acoustic showing those two systems.
The skeleton of a classical guitar will be quite different because the bracing pattern is different, but the broad strokes will the same: There will be the strings, the bracing, and the saddle serving as the interface between the two.
This suggests that a cheap saddle will be very detrimental to a guitar's sound, that throwing out that piece of plastic and getting bone or tusq is worthwhile because the saddle is actually a critical element in the transferring of string energy to the top.