TLDR: difficulty settings need to, but currently do not, affect certain critical aspects of fight difficulty like the speed/timing of mechanics, and there should be a toggleable "story only" option independent of difficulty setting that stuns you whenever you take lethal damage but ultimately does not kill you.
It's kinda wild that the MSQ is mostly point, click, watch cutscene, maybe fight an enemy or 3, yet it's got solo duties where the responsibility for success rests ENTIRELY on the solo player's shoulders, with mechanics meant to challenge average able-bodied players, but there's no way to make them more accessible to certain folks who can otherwise engage with every other part of the story just fine. At least in dungeons/trials, there is always the option of having other players help you. I guarantee if you put a PF up or shouted in Limsa that you're having extreme difficulty getting past one of the non-solo MSQ duties, there are a wealth of players who will actively want to help you and would happily carry you through the roughest bits if necessary so you can continue the story.
Upon reviewing a YouTube video of this particular battle, it seems deliberately designed to nuke your HP at certain intervals, then lay off the damage to give you time to heal up from your skills. For example, the first big damage is an unavoidable AOE that chunks a good 70% of your HP within a few seconds of the fight starting. After this, however, Bakool dashes to the edge of the arena and starts casting. He does 0 damage for around 12 seconds and by the time it goes off and he starts auto attacking again, Wuk has had time to heal and her HP is now at a slightly cozier 50%-60%. The fight more or less continues in this pattern of beating you down but letting you crawl your way back up, presumably to make us feel the same kind of pressure and stress that Wuk's feeling, and maintain that energy throughout the fight. Personally this duty was a thrill for me, I felt like I was barely scraping by the whole time (which I thoroughly enjoyed).
That being said, I'm an able-bodied Savage/Ultimate raider with a very high skill level, and I'm very much used to reading and resolving mechanics without stopping my rotation, hitting my oGCDs when they come off cooldown (offensive) or when they're needed (defensive), all while under continuous pressure not to f*** up. I personally enjoy that and derive satisfaction from that. But not everyone does, and that's okay! XIV's mandatory story content should be accessible to the vast, vast majority of players.
What's striking to me is people in this thread saying Easy and Very Easy don't seem to actually make the duty easier in the ways that matter most, and they note the timing of certain mechanics is still very tight regardless of difficulty. If this is true, imo it's unacceptable in modern XIV and absolutely needs reviewing by the developers. Most of modern FFXIV's difficulty comes NOT from "how fast can you kill the boss" or "how much damage can you tank before dying", but rather, "how fast can you figure out where to move/stand, and how quickly+precisely can you pull it off". If someone is disabled, and said disability affects their ability to process mechanics and/or react to them accordingly, they are going to have a horrible time regardless of how beefy their stats are. The easy difficulties should not only buff the player's max HP and HP recovered from heals by a significant margin (leaving more room for mistakes), but also slow down the timeline of the fight (or at least specific mechanics) to reduce the overall minimum execution requirement. And, of course, there should be a "story only" option that's independent of difficulty setting, wherein taking lethal damage will stun you for a few seconds, but ultimately let you continue the fight.