The original Orville Gibson guitars had glued down bridges.
What Mike said: glueing down the bridge and tieing the strings to it torques the top, and you have to make it heavier or add bracing to withstand the load. Why not take advantage of the geometry and just use a tailpiece?
An article in the recent 'VSA Papers', the putative replacement for the old Catgut 'Journal', claimed that the twice-per-cycle tension change in the strings could drive a violin top. The language in the article is vague, but basically it's because the strings are not parallel to the plane of the top, but at an angle. Changes in tension push down on it. This is the main 'benefit' claimed for flat-top type bridges, and it may bnot be all tat much of a difference after all.
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