Too often the dungeon / normal trial & raid tank busters are just down time for everyone involved (there are some exceptions). They really don't hurt a mildly geared tank who used the appropriate CD and as a result the healer can pretty much ignore the tank during them. The DPS just have down time either way, and not every boss (especially once it becomes old content) needs to have that.
Suggested change for Dungeons / Normal Trials & Raids:
Starting at the fights first tank buster pair it with another party mechanic. It doesn't have to be a totally new mechanic, it could be one of the mechanics the party has to deal with anyway, except it's timed to go along with the tank buster.
This gives the tank a small level of threat because if you mess up the mechanic, you're hit by both at the same time. Because the threat is higher (even if slightly) to the tank, the healer needs to pay a little more attention. Lastly, both the healer and DPS are given something to do during a tank buster.
Why this change?
Besides the reasons mentioned earlier about keeping players engaged while content is current, it also stops a boss fight from becoming too passive once the content gets old. In older fights, the downtime during a tank buster usually means nothing really happens while you DPS it down resulting in other more engaging mechanics being skipped and that makes the whole thing way less fun. Even if the mechanics are simple, having something to do is always better than just sitting around and if I'm being honest, there are some mechanics I really appreciate the time / effort the dev team put in but once the content is old they're never seen again.
Does stacking the tank buster with a mechanic solve every issue of old content being too easy? No, but it's a small start that makes current and old content more engaging without altering the difficulty too much from the dev's current target. Some of the fights already do this (not enough though), while other fights the boss may not need this but could use a simple buff to give it a little more damage and HP (looking at you Ravana).
This suggestion isn't meant to be mind blowing, it isn't meant to radically change the fights, nor is it meant to drastically increase difficulty. It's just something to keep you a bit more active while allowing you to retain more of the mechanics in the battle as the fight ages.