What tenacity does is fine. It's the scaling that needs to change. Piety should cover a similar range of functions (i.e. attack potency, healing potency, and MP regeneration rate).

Now if you want people playing these roles to pick these stats, there are a couple of things that you can do.

1) Make these into Primary Attributes, and just standardize the stats across all roles. In other words:
Tanks: Tenacity (Attack, Defense, HP restoration/Lifesteal)
Healers: Piety/Mind (Attack, Healing, MP regeneration)
Melee: Strength (Attack)
Ranged: Dexterity (Attack)
Magic: Intelligence (Attack)

Secondary Stats (Everyone): Crit, DH, Determination, Haste

Why do this? Well two reasons. Primary Attributes scale with ilevel, so better gear scales up all of your essential tank functions. Second, it decouples tank attribute progression from melee dps, so you don't have to worry about tanks having to gain Strength more slowly than Melee DPS to keep us from outperforming and embarrassing them, Heavensward style.

2) Make all Secondary Properties have diminishing returns. What do I mean by this? The opposite of how Crit gains value. Ideally, you want it to be such that you gain less of a dps boost per additional point of any individual stat. This encourages you to diversify your stats, rather than dumping everything that you can into Crit, followed by the next most effective stat only when you have no more room left for Crit. So even if we go back to that idea of Tenacity and Piety providing the 'best' damage boost for tanks and healers respectively out of your secondary stats, the gain drops off as you invest in it, suddenly making say Crit and Det better. Now you start investing in those but the relative gain falls off, meaning that you gain more from stacking Tenacity.

And note that none of this actually impacts the relative dps that tanks and healers do compared to other roles, so long as you can control the relative weighting of each Primary Attribute. Your Secondary Properties are a drop in the ocean by comparison.

Smart players are not going to want to invest into a 'defensive only stat'. We've seen this, it was called Parry. They are also not going to want to invest in a defensive stat that provides inferior offensive gains to its counterparts. They certainly will invest in a defensive stat that provides better offensive gains to its counterparts, even if that only occurs at set stat intervals. The main thing that everyone wants out of a stat system is to gain progressively stronger offense with better gear. We don't want dummy stats like Parry and Accuracy that occupy equipment slots without providing an offensive benefit. We also don't want inferior offensive options like Tenacity is now, even if it comes with a swiss army knife of helpful secondary functions that you can live without. Nobody likes feeling shortchanged on their gear upgrade.