Why do LEO constellations require orders of magnitude more satellites than a GEO system?

The Earth's rotation carrying the user out from under the limited view

The primary reason Low Earth Orbit (LEO) systems require orders of magnitude more satellites than a Geostationary Orbit (GEO) system stems from the dynamics of the Earth's rotation relative to the satellite's fast movement and small coverage area. Because a LEO satellite has a narrow visible footprint and is constantly moving rapidly across the sky from the perspective of a ground observer, the user is quickly carried out from under that satellite's limited view. To maintain continuous connection, the constellation must be tightly interleaved so that a second satellite is already visible before the first one sets below the horizon. This rapid turnover due to Earth's rotation, coupled with the small coverage footprint inherent to low altitude, mandates thousands of units for a comprehensive, uninterrupted network, unlike the few slow-moving giants needed in GEO.