Br*** is a softer metal and it will take the wear when you engage the sychro therefore saving the gear. Cheaper to replace sychro rings than gears.
In that particular application, I guess the synchro's br***/bronze (or whatever it is) wears better against the steel (some kind of steel) cones and the steel cones wear better against the br***/bronze. Steel synchros against steel cones might destroy each other? and be very noisy in the process?
Best combination of wear resistance, friction coefficient and lubrication retention. Same reason its used for bearings.
My guess? Probably due to the ease of machining the wear and working surfaces coupled with long life. The inner female cone surface is carefully shaped to slip and not slip at the right times, lots of little grooves. Probably hard to do with other metals/alloys. And if steel they would wear into the more expensive parts, main drive gear and other gears.
The br*** rings are cone clutches that speed up or slow down the gear selected so that you can shift with no clash. The teeth on the rings prevent the shift until the selected gear is turning the exact speed as the main shaft. I think br*** was chosen for it's wear resistance in this application. You could probably use some type of clutch material, but bonding might be difficult. I think I have seen some plate type syncronizers that do use clutch material. Chrysler used the plate type syncronizer in their early transmissions.
Syncro is essentially a friction clutch. If made of steel there would be a high likelihood of galling when engaging the gear. Br*** is a dissimilar metal which makes that unlikely, and presumably has the desired amount of friction to do the job.
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