Placing offensive and non-offensive resources on the same cooldown will always result in offensive resources being favoured. This is an immutable consequence of this game's combat system.

Mitigation tools that cannot be relied upon are worthless. A decent healer will have planned how to complete a fight in advance, making extra RNG mitigation unnecessary. Unless the extra mitigation can save a healing GCD it confers no benefit, and even with a beefy -20% mitigation this is unlikely to happen outside of intense healing checks like J Waves or Terminal Relativity. This stems from how damage in this game tends towards infrequent spikes that must be mitigated to survive. If the game treated HP as a resource that is consistently drained and must be replenished using finite healing resources (like in most other games featuring healers) then RNG mitigation gains value in that it conserves resources. Utility, such as MP regeneration, falls into the same trap unless it can be converted into damage.

Unless you want to make a portion of cards entirely worthless there is no way to implement them as anything more than an offensive tool without either overhauling the entire combat system or splitting AST's cards into offensive and defensive decks that are accessed using two separate resources.