The softer materials make for a more forgiving assembly.
For perfect fit with bronze washers, your holes will have to be dead on and your spacers the precise width required, otherwise when you cinch down the pivot, the liners deflect and are no longer parallel. This means the washers aren't making full contact between the blade and the liners resulting in increased wear and general potential sloppiness in the action--especially as the washers wear. With rigid washers, just about any deflection will result in this condition to one degree or another.
A big benefit of using teflon, nylon, etc is that it squishes down in the assembly so you can take up this deflection between the liners without the pivot feeling excessively tight. The washer conforms.
One drawback is that the assembly is not as rigid as a good-fitting bronze-bushed one. Also, Teflon and nylon will not last nearly as long as properly fitted bronze.