My concern is how are Allen keys rated so that you might know their torque capability prior to getting into what brewnog describes...
Allen keys aren't rated unfortunately. If you look at the size of the key compared to the size of the cap screw (for standard sized cap screws)*, you'll find the key has a dimension across the flats roughly equal to, or very slightly smaller than, the minor diameter of the thread. The key however, is generally of very high strength steel, even higher than a bolt, so in generally the key is strong enough to torque a cap screw right the way up to the point of breaking. At this point, depending on the strength of the cap screw, the Allen key may also be very close to breaking, so which one breaks will depend on material strength among other factors.
There are other factors however. The head of the screw creates friction with the parts being bolted such that the screw head can resist some torque without transfering that torque to the threaded portion of the cap screw.
In general, Allen keys should hold up to the torque requirements of the cap screw. Given the example provided, (a 3/4-10 UNC cap screw torqued to 387 ft lb) the shear stress in either part is unusually high. I could see either part shearing.
Before such bolts shear however, I've generally found the Allen key gets rounded off, or the cap screw socket deforms. If you're experiencing failed Allen keys or rounded off parts, it may be because the torque specified is too high.
*Note: Although standard sized cap screws should be ok, many of the low head cap screws have minor diameters much larger than the Allen key, such that the Allen key is much more likely to fail in shear. You may want to clarify if standard or low head cap screws are being used.