It’s all down to inertia! Adding weight to the bridge (e.g. brass rather than plastic pins) slightly changes the way/the extent which the bridge moves the guitar top. I doubt it matters what the pins are actually made of or, for that matter, whether the weight is actually in the form of bridge pins. It’s just that changing the bridge pins is probably the most elegant solution.

A luthier friend of mine once gave me a set to replace the mass lost when he had shaved the top of the bridge down. I never used them but he used them all the time on the guitars he built.

I recall that, back in the 70s, Frets magazine did a series of experiments hoping to draw some conclusions on the then current fad of fitting brass nuts. They eventually decided that it was all down to weight. Add weight to the end of a guitar neck and it increases sustain but you needn’t bother with the luthiery; simply adding a G-Clamp to the head would have the same effect.

None of this can be said to actually “improve” the sound of a guitar, all it does is change it and it’s all down to personal preference.