If the triangles are completely removed the seam will have nothing to "grab on to" at that point in the top layer. The seam is right at the base of the triangle, so if you remove the triangles the seam will be freed up and have nothing to hold on to on that layer.
It's like if you cut off the seam allowance on fabric - if you cut *right by* the seam, it will just fall off since it will no longer be between material.
Losing that seam may or may not have an impact on structural integrity. You might be able to glue down the material that's been freed up ad well or have someone re-stitch it with a normal edge.
Actually in the pipes:
- Remaking Ser Loras doublet.
- Luke Skywalker, A New Hope
- Wind Waker starter costume in swim material
Eventually: Paul from Dune, Faramir, Harry Sullivan