Siyahs and static recurves are designed to give the bow extra power in a shorter overall length; even more power than a 'working' recurve, because each siyah/static tip acts as a sort of atlatl to boost the power at the the release.
As mentioned, siyahs on Asiatic composite bows are thin side-to-side, but thick from back-to-belly because they are designed to work with the powerful wood/horn/sinew composite bow (80-140# draw). The thin all around, but rigid lever tips of the Mollegabet/Holmegaard selfbows are not intended for nearly that much power. IIRC the archeological originals are estimated to only be in the 30-60# draw range.