I feel like I overall understand where you're coming from. Doing a static rotation can feel stale, especially in a game where you are so seldom needing to change your rotation in any meaningful way in response to what happens during encounters.
That said, I feel like we should be very careful where we inject RNG into player's kits. For example, does randomizing whether I should press 1-2-3-4-5 versus 1-2-3-5-4 actually result in a more enjoyable play experience? Or does it simply add unrewarding busywork? Not everyone is going to agree. And I'll posit that the reason that not everyone is going to agree is because at a fundamental level, this interaction itself isn't innately fun; rather, it simply feels like a breath of fresh air to players who are so stifled by doing the same static rotation for years that even the most minor step away from that tastes like a feast. We can do better by focusing on what would be more universally enjoyable.
Personally, I hold up Thunder procs as one of the best uses of RNG, but I think it's so important to understand the context it exists in, because that's the reason it works so well! BLM is constantly juggling multiple timers to keep their plates spinning, and to do this they need to make sure they cast certain spells within certain windows. Cast too late and your plate falls on the floor, cast too early and you're losing some of your potential damage output. Because of this, BLM needs to actually consider and react to enemy behavior when determining what they will cast and when, because their cast times means they can't just change tactics on a dime without making sacrifices.
And it's within all this layered management and potential for failure that Thunder procs shine. Because you want to cast them ASAP, both because it feels good to press the juicy damage button and because the sooner you press it the sooner you can get another proc for even more damage. But these procs also require that you change your plan of how and when you're going to spend your resources in the limited time before your plates need another spin, which can be a challenge. So opting in to press this juicy button comes with a cost that you may not always be able to pay, and sometimes you may drop a plate you took a risk that didn't pay off.
I initially started writing this to hold up how Thunder does RNG right, and how that implementation probably has something good to learn that we could apply to other classes when using RNG. But in writing this, I think I've come to a different conclusion. Because RNG in and of itself doesn't make Thunder fun; rather, it's the potential for failure that makes RNG fun. If BLM couldn't drop those plates, then Thunder would just be a spell that periodically inserted itself into your rotation...and that's not very compelling. But since BLM can drop their plates, Thunder allows them to take a risk that will give them more damage if they succeed...with the potential outcome that the BLM bites off more than they can chew and all those plates come tumbling down.
So my updated response is this: we shouldn't be adding RNG to classes, we should be adding opportunities for failure into rotations in the form of risk/reward mechanics. Maybe those will have RNG, but maybe they won't. I'd hazard there are a lot of different ways to do that.
Anyway, food for thought! ^^