Eternal Life does not work intuitively with Sanguine Diviner

Maybe it is intended, but for sure it does not make sense that Eternal Life can make your character not play with an upgrade.

I am playing Lich and just dropped the Unique Sanguine Diviner that has:

25% of Spell Mana Cost Converted to Life Cost

It was a upgrade for my build because it had more Spell Damage than my previous wand.

You would believe that with Eternal Life you could make your skills cost less, because you try to pay the cost but the passive would stop you from losing life.

But actually what happens and is not described on the skill is that the game treats your life as ZERO and so you can't pay the cost on any skill that requires mana, because with Sanguine Diviner all your skills requires a portion of your life.

That behaviour also happens with Lifetap, that maybe could be for balancing reasons but is also not intuitive. The game should warn you of such gimmick or should fix so Sanguine Diviner works with Lich.