Repeatedly removing those edges would help indeed! I am interested in finding the loops, but in the example provided the "dead end" edges do not contribute to the loop. Officially a loop is not allowed to contain the same vertex twice (besides start/end), otherwise any sequence of vertices could be considered a loop just by repeating them in reverse order.

However, indeed it remains true that it does not find all loops, only the smallest set of loops that cover all edges.