How Battlemage rune enchant mechanism works? (Lightning strike warden)

Hi,

I can't find a proper answer for this.
I purchased an imperial claw with added fire, cold and lightning dmg for my lightning strike warden build. there is a Battlemage rune enchant on it, which costs more than 5 divs.

since I'm still lacking the full understanding of how added elemental damage works (is it spell or melee dmg?), I'm not sure, if I get anything from this battlemage enchantment, since it adds to spell dmg. So I don't know, I can remove it, or which rune enchant could give more dps to the claw attack dmg.

Battlemage allows casters to benefit from their weapon damage. It's useless for attackers.

You can craft the last tier of regular added fie, cold or lightning damage.
Values of local crit chance and attack speed enchants are tiny but probably can compete with added elemental damage on high-end claws.

Situationally useful rune enchants for claws:
Melee Strike Skills deal Splash Damage to surrounding targets
% increased Rage Effect
Enemies Killed by your Hits are destroyed

Thanks MonaHuna, I had the same feeling, but the enchant was too expensive to just change it. I will definitely try Rage effect or stick with regular added elemental dmg