My opinion is that regarding use of via ferrata set there really is more room for "debate". Everyone equips as they think they should or don't need to

... hope based on experience, physical ability, psyche.
Regarding helmet no dilemma, under walls, in rocky terrain it's mandatory.
Don't know why you'd bash helmet into rock, if it happens, helmet at worst cushions the blow, if sweat runs down face equip with sweatbands, headband, cloth etc... Why would via ferrata set get caught on peg or rock? When not in use it's clipped to harness loops, when climbing you need to be fully concentrated and focused anyway.
True, accident never sleeps. Even the best equipped and prepared can have it happen... but that shouldn't be "excuse" not to equip properly.
Good luck!