There's always going to be the problem of "as long as there is a card that increases damage the most, it will be the best card and all other cards will be meh if not terrible." You have utility cards here, which is great and fine, but people will still choose / fish for the damage cards instead.

If people really want utility cards AND damage cards, then maybe it would work if there were two separate Draw skills for them that don't share a cooldown with each other or anything else.

nb4Mitsuki