I was asked whether a wide bridge covering the piezo under the lid will sound different than a bridge covering the same area but with gaps as seen with three contact points?

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An areally wide bridge is important for driving a large soundboard. You need to scale the bridge down substantially, in terms of surface area, to drive the much smaller soundboard of a cigar box top or bottom. You can concentrate that driving force by using a footed bridge, similar to those used on mandolins, violins, violas, and even standup basses. Significant bridge height will increase the break angle from tailpiece to bridge, resulting in greater force applied to the soundboard. Having a footed bridge further concentrates those forces into the soundboard, exactly the same way a flying buttress on a medieval cathedral transfers the downward force of the roof from the walls to the ground.

And a floating bridge allows you to set relative intonation and string compensation pretty quickly and easily.

like most things it's a balancing act

the bigger the footprint the bridge has on the soundboard, the more it dampens the sound, just like adding more bracing on the underside.  the smaller the footprint the bridge has on the soundboard, the more likely it is to crush into and dimple/divot/gouge the soundboard. 

commercial acoustic guitars have that big rectangular bridge because anything smaller would not be able to distribute the tension load enough, it tilts forward distorting the face and then the glue partially gives way and the ply delaminates and it takes some wood with it and at that point you salvage parts ( sad story from my teen years )

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