I think there's some correlation. Possibly analogous to a flywheel. If you make a flywheel too light, it will be very easy to start, but at the same time very easy to stop. On the contrary, a very heavy flywheel would be difficult to start, but at the same time slower to stop.
At the same time a denser bridge may lead to more sustain, but may act as a ballast, keeping most of the energy in the string and transferring less vibration to the top. Conversely, making a bridge too light may allow a quick transfer of vibration, yet have very little sustain.
The final aspect is hardness of bridge. A soft bridge may damp some high end, a bridge of steel may be overly bright.
I would hazard a guess I'd want a bridge where the graphs of these three variables converge ...
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