Fixed-point barrels have the point pressed in under real force, and a proper repointing tool is what pushes the old one out and the new one in squarely.

Squarely is the important word. A point pressed in by hand goes in at whatever angle you managed that time, and three darts with points at three slightly different angles will never group properly however well you throw.

The tools here are built for repeated use rather than one job, which makes them worth having if you repoint for other people as well as yourself. Screw-in point systems use a key instead — Swiss Point, Quick Point, Switch and Rapid each have their own.