Idol based procs also don’t work independently for each hand when dual wielding. I just tested 15% spike totem proc chance while using the unmodified swipe. There is only one hit that combines the two weapons.
That’s the thing, in LE, your skills do the damage & you only use a skill once so you only get one lot of procs. If you’re DWing, your skill will have much higher damage than if you’re just using a single one-handed weapon, that’s where the benefit of DWing comes from, it’s not that you get a second use of a skill (once per weapon).
If there’s skills where the animation doesn’t show the character DWing when they have two weapons equipped, that’s a different kettle of fish.