Esuna could very easily become a more prominent mechanic if they just updated the UI on debuffs to be very visible and easier for anyone to notice. I've brought up the FFXII example many times before, but something like this would instantly make Esuna debuffs clear and identifiable to any player:
Esuna is tricky though, because some debuffs aren't worth using Esuna on while others must be Esuna'd, like Doom, but there are things that you could do to make it more interesting and more of a decision healers need to make. For example, if all instances of Doom can either be Esuna'd or removed by healing someone to 100%, you have 2 routes to clearing the problem. Healing it off with OGCDs is the better solution, but might not be as easy in certain scenarios. And if you're dry on resources and need to spam something like Medica/Emergency Tactics Succor to remove it, Esuna now becomes a better alternative potentially.
Or if we look at other debuffs... Heavy for example doesn't need to be removed, but if it's applied during mechanics that aren't impossible to do while heavy but are otherwise more challenging, you have a decision to make, including potentially using Rescue instead of casting Esuna. Paralysis as well isn't always a detriment to physical jobs, though is very helpful to remove off casters, particularly BLM.
EDIT: This also means that Esuna utility on other roles can be actually helpful and another way to help diversify other roles. Bard being able to remove debuffs for the healers can give them a niche that goes beyond raw damage over Dancer and Machinist, but you'd also want for Dancer and Machinist to also have other advantages that Bard does not have where each of them can thrive.