It was a question of international law, especially of the Hague Convention of 1907. The Flieger-HJ were part of the civilian population and that's why they were not allowed to fight in acts of war. Taken captive in fight, it would have been legal to execute them by shooting. The Flakhelfer/Marinehelfer in contrast belonged to the fighting troops, so they ended usually as PWs. But their uniforms were very similar. Axmann personally insisted on the HJ armband (matter of power), the Minister of the Interior suggested an additional yellow armband. In July 1943 Hitler personally decided (no surprise) that there was "no need of marking the Flakhelfer as combatants".
So only the LWH badge and (in fight) the steel helmet were the Luftwaffenhelpers' signs of belonging to the fighting troops, but of course they were combatants. And Wehrmacht and Kriegsmarine wanted to guard them against above mentionend danger. Maybe (I assume) that's also a reason for differing shoulder straps (no number), and there was no further need of wearing an armdreieck (Boys from different regions served on the same air base, Bavarians, Silesians, Pommeranians etc, and relocations were non uncommon, so it would have been a senseless mixture of armdreiecke). They were soldiers-like now.
(Source: Nicolaisen, Flakhelfer, p. 183ff.)