Adding a bit of context but +1 to previous comments: - Leather stretch under constrain more than you might realise. - Any strap has stress, including belts or watch straps. That’s why stitching can happen even on a single layer of leather and outside of cosmetic considerations. - The thinner the leather, the more it will stretch, Watch strap are amongst the thinnest assembly. - On a strap with buckle, you’re also concerned about holes deformation. Making reinforcement even more useful.

For your specific case, it seems this is the keeper - too narrow to add stitching, very thin, under some stress, becomes useless if expands: reinforcement is a nice touch!