In addition, Shiva has a level of randomization as well, though in her case it's a coin flip between sword and staff forms at certain points.
Sort of. There's also randomness in whether or not she does certain minor attacks (When - or even if - she does Heavenly Strike during Sword Phase, for instance).

The major concern they had with randomness in boss rotations in super high level content is the concern about "okay, so there's this really hard combination that can occur and so this group just retried until they got a run without it and won". Consider for a moment if, during Titan EX, you could get back-to-back plumes at any time - including while you're busy dodging a set of bombs (oh god that sounds horrifying). If that sounds like a nightmare... don't worry, eventually you'll just get a run where you don't have it happen!

And there is some aversion to randomness among the player base - see the reactions to Thornmarch EX. About the only rules to what can happen in that fight are that there's x attacks during the first phase and an additional y that can happen in the second, and that they won't repeat. For a long time I heard a lot of people saying they'd never touch it again after getting their clear.