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Why are long-period comets believed to come from the Oort cloud?

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asteroid Ida and its satellite, Dactyl — Small body Asteroid Ida and its satellite, Dactyl, photographed by the Galileo spacecraft on August 28, 1993, from a distance of about 10,870 km (6,750 miles). Ida is about 56 km (35 miles) long and shows the irregular shape and impact craters characteristic of many asteroids. The Galileo image revealed that Ida is accompanied by a tiny companion about 1.5 km (1 mile) wide, the first proof that some asteroids have natural satellites.

Long-period comets are believed to originate from the Oort cloud primarily because of the distribution of their orbital energies.12

When astronomers project the orbits of long-period comets backward in time, they find a significant excess of comets with orbital semimajor axes larger than 20,000 astronomical units (AU). This concentration of distant orbits suggests that these objects are arriving from a vast, spherical reservoir of icy bodies surrounding the solar system at these extreme distances.123

The Oort cloud is considered the only viable explanation for the observed number of comets with such distant, gravitationally bound orbits. These comets are typically "new" to the inner solar system, having been perturbed from their distant, stable orbits by the gravitational influence of passing stars or the tidal forces of the Milky Way Galaxy’s disk, which send them inward toward the Sun. Once they enter the planetary region, the gravity of the giant planets—particularly Jupiter—further modifies their orbits, either capturing them into shorter periods or ejecting them from the solar system entirely.312