I'm actually surprised I've not dug into this thread sooner tbh, it's a pretty important topic all told.
It could definitely (and probably already has) be argued that part of the blame of this lies in the combo of heals being incredibly potent and non tanks being incredibly squishy vs boss attacks. However, I wonder if this could be mitigated if SE were willing to shake up their encounter design somewhat.
To simplify what we have now, your typical garden variety FFXIV boss will usually consistently autoattack whilst following a scripted sequence of special abilities with little variance. Key points of damage are usually rather predictable leaving healers and tanks free to stretch themselves thin in safety whilst spamming DPS to fill in the very large gaps.
IMHO this often leads to rather tedious encounters if the designer doesn't force a bunch of movement in with the scripted abilities (Compare A9S with A10S for example) and I also feel that plain jane auto attacks are also a bit of a wasted opportunity as well. Having auto attacks proc additional cleaves and aoes would do wonders for preventing us from simply throwing a medica II up and ignoring the fact that the raid as at 20% for the next 20 seconds as is frequently the case now.
It doesn't even have to end there. Everquest had a rampage mechanic where the boss would have a secondary target and randomly pummel them as well as the MT. FFXI had a wonderful gimmick where large 4 legged mobs and bosses were able to attack with any limb without the need to spin on the spot. Dragons didn't visibly spin around when someone pulled agro, they simply and subtly kicked away at them. Given that SE had that 10 years ago, it has me wondering why we don't have Dragon's hacking and kicking away at the raid around them in 2017?
There's so much potential to make bosses both mechanically and visually more exciting that's wasted every time we get some goliath thing that simply sits there firing laser beams and parping a rocket out every 30 seconds (</3 A4S).