There is something that actually played no small role in randomness back before Stormblood, and that is only found on a smaller scale currently on Ultimates due to phase transitions: the mechanical script of bosses used to be HP based and not fully time based only. This meant that if your party reached a specific HP threshold, the boss would start a new series of mechanics earlier. It introduced some issues like totally skipping a mechanic halfway through but this was mostly notable in complete overgear or unsync scenari, which don't really matter in terms of full fight experience anyway. Still, SE decided to do away with it because 1) it served their agenda of now allowing players agency whatsoever and limiting skill play and 2) fixed the aforementioned unsync issues.
Combined with the pseudo random phases that we sometimes get in fights like Guardian (the most complex up to date with this), or P8S doorboss, this can truly shake things up and make runs feel more different from each other. SE also does have the tech to let mechanics run their course before switching to something tied to a HP threshold, as shown in the recent M4 Arcadion fight, where the boss below 15-20% HP or something starts to cast the soft enrage cannon shot that never ends: if the boss is still in the middle of a wide mechanic, it doesn't stop it but goes to its end before switching to the threshold mechanic (soft enrage), which allows for a smoother and more natural transition.