This is all spot on. Sails fail due to wear of the fabric itself, because a seam failed, from rubbing, repeated stretching and releasing (you can tell an older sail because it will bulge more as a result of this) or because it got over-stressed. Salt water obviously also doesn't help with sail fabric longevity, as does UV influence all of which will age a sail (check the color difference on spare sails that have been bagged vs the ones in use or, check the first strip of a roll-up sail to see how much that can affect the fabric).

Those areas where the sail needs to be strongest is where they are re-inforced doubling up the layers (and not just 'two', a corner can easily be 10 ply or more thick), on older boats further re-inforced with leather or heavier grades of fabric. The panels are carefully laid out so that the highest stress aligns with the warps. A large sail can be made up from many 10's of panels, which are joined in a variety of manners (glue (typically for very fast boats or as re-inforcement of stitching), stitching, sometimes ultrasonic welding for special applications). On the very high end there are even laminated custom laid out fibre pattern sails (for instance: a sandwich of Kevlar wire between two layers of bonded fabric or plastic).

At one time I worked for a competitor of North Sails, who by the way were pioneers in the digitization of sail manufacturing.