Bridge thickness
 

Why is a bridge as thick as it is generally accepted to be ?
Of course , there needs to be sufficient mass to support the saddle/s .
What about elsewhere ?
Is the thickness as it is rearward of the area that supports the saddle/s the way that it is simply in order to provide a mating/anchoring surface for bridge pins ?
If bridge pins are not used , is this area necessary ?
The majority of pinless designs anchor the pins to the bridge rearward of the saddle and from above the top . This necessitates the required material to provide support for the task of anchoring the strings under tension .
Should the strings be anchored below the top , this material seems to be unnecessary .
The material used to anchor the pins or support the string ends becomes purposeless mass . Because of this the bridge can be trimmed to eliminate this now unnecessary mass or am I wrong about this ?
Please keep the accepted idea of bridge/neck geometry out of this . I am not questioning that . I am only questioning the area of the bridge itself behind the saddle/s . Yes , they are 2 separate things .
Let the slings and arrows fly .

A good question, but I would like to take it a step further - how relative to tone is bridge mass in general? Does some mass actually add to the tone? what if you could make a bridge that had the structural integrity needed, but has no mass, how would that affect tone?
There is a noted difference between Ebony and Rosewood bridges, with Rosewood being a bit lighter. If mass is a hindrance to tone, why not hollow out, or otherwise lighten the bridge?

I think it's mainly an artifact of mass production. Blocky bridges take less steps to shape, and are easier to clamp since they don't want to slide forward like a wedge shaped bridge.

I always use wedge shaped (with pins), and haven't had any problems with it. Only the part in front of the saddle slot needs to be full height.

Ebony is more dense than rosewood .
The static load on a bridge is something that needs to be considered as well .
Would a more loaded and lighter bridge be equal compensation for a less loaded and heavier bridge .
An example can be found in auto racing where lighter vehicles are loaded through aerodynamics that effectively make parts of the vehicle heavier/more loaded .
Convert this to a guitar where a lighter bridge can , through loading , do what the heavier bridge does with less loading . Heavier loading can be obtained through greater break angle , thicker strings , longer scale , combinations of these ...........

I'm having a hard time understanding the question, in particular this,

"The majority of pinless designs anchor the pins to the bridge rearward of the saddle and from above the top "

Is it pinned or pinless???

I'm thinking you are talking about the belly? The part of the bridge that is rounded out behind the pins when looking from above?

If so I believe the primary reason for that was to give the bridge a larger foot print for it's gluing surface. It also rounds out the stress caused by the bridge rotation too. In cross section it's typically rounded out like an airplane wing. That reduces weight and feathers off an abrupt stress riser as well.

I suggest that the bridge is the way it is largely because it is known to work. By using what is tried and true, one eliminates/reduces the risk of failure.

For most designs, the bridge is the largest, stiffest brace in the central area of the guitar top. That stiffness could be achieved by other means than a large, heavy bridge.

Theory suggests that the response of the instrument is related to stiffness and mass. Typical bridge design offers one range of combinations of those two variables. One could create a new bridge design with a new balance of stiffness and mass, though the resulting response is unknown.

As I've reported before, in the late 1970's Charles Fox made a guitar with 6 small, individual bridges, one per string, one per bridge pin. He told me that he found the sound lacking sympathetic resonance.

Kasha/Schneider went the other way, with a much larger bridge in which one half was tall and narrow (stiff/low mass) and one half low and wide (low stiffness/higher mass), split in the middle to allow independence of each half. Back in the day, a fair bit of work to make that style of bridge, though it looks "modern" and interesting. (With today's CNC machines, the added work to make the bridge is, for many, irrelevant.) I've changed too many variables to say what result the bridge, itself, has on the mix.

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 ...

Now all we need is the graphs. ;)

In general, the lighter the bridge, the less sustain you'll have. The heavier the bridge, the more sustain. (Try brass bridge pins and brass saddle for an experiment.) The tone that has become acceptable and desired is one that calls for a standard range of bridge mass. This is part of the issue.

Both and all of them .
Parsing this into separate items is not where I am going on this .
I'll try again .
What is the reason for a bridge to be 3/8" or 11/32" thick/deep behind where the saddle/s are located ?

Must that weight be contained totally within the physical bridge itself ?

Not sure... I've been tapering the backs of my bridges along with the wings, but my bridge has a slightly wider footprint that splays toward the wings as well.

Mainly for strength. Anchoring the strings under the top (with or without bridge pins) means there is stress in one small area that is more than the top itself (or the top plus a conventional bridgeplate) can handle.
You can shift some of this structure to the underneath side of the top, in essence producing a two-piece bridge.
While trimming some off the lower half of the bridge is possible, there is a point where you are compromising the ability for the bridge to hold the saddle upright.
Low mass (hollowed out) bridges have been tried, with mixed results. As the bridge weight is reduced (particularly as a proportion of the total top weight), the guitar tends to sound more and more like a banjo, meaning louder but with less sustain and less pleasing tone.

A lot of the detrimental effects of string tension and torque/loading is transferred directly to the top plate, through the bridge, and bridge plate. What if part of that loading and stress could be re-applied to the x braces directly? I am thinking of a cross brace located where the bridge pins are located - a brace that has it's ends resting on top of the main X braces. that way, the pull is not on the top directly, but rather acting directly on the main braces, which then cause the top to deflect and vibrate.

Stiff rather than soft. Also the same size bridge for an 0 as compare to a dred? Should it not be lighter? But if you have the same scale length maybe heavier bight be the part of the answer to get some bass response? Just taking mass into account the main resonance peak would be less with more mass, less responsive but a more even note response. Would spreading out the mass and stiffness give you a better response or if the bridge takes up more area will the high frequency nodes change, actually be smaller than if you had a bridge with a lower footprint? What was the original question again?