That is correct, it protects the wire in case of a short circuit. But wire is rated for its amp carrying ability, as this link at Blue Seas shows.
Electrical Properties of Standard Annealed Copper Wire - Resources - Blue Sea Systems
Distance doesn't relate directly with current carrying ability of the wire which is not variable. But voltage drop does vary greatly with distance, most of which I try to keep to 3% or less, even for lighting. The fuse or breaker for a given wire size should not vary with distance on a given gauge of wire. The wire gauge should certainly vary with length however for a specific load.