Indeed, some cameras do need the leader. Usually they are manually loaded and winded - they use take-up spools with a slot for the leader. Advancing the film is performed by turning the take-up spool, and sprockets alone would not provide grip secure enough. For example, Bronica 135N/135W, Nikkormat EL-W.
When the film has been fully rewound into cassette, retrieving its full-width end would be tricky as you'd have to perfectly align the end inside the cassette to the opening; retrieval of a narrow leader makes this awkward task much easier.
The leader (albeit in a much longer form than on most currently produced films) is also useful for correctly loading film into a bottom-loaded camera (such as LTM Leica, FED, Zenit-1 etc) so you wouldn't have to align the film cassette, take-up spool and bare film all at the same time, which would be quite clumsy and prone to fail.