The Shadowbringers 2-minute meta is tied in with a lot of the job homogenization over the last 3 expacs. Every job wants to align buffs, so every job is given a buff on a 120 second cooldown and gets designed to feed into that 20 second burst window without deviating. Any kind of global drifting that places your burst window out of alignment means lost potency.
As others have no doubt pointed out, parsetrannies and raiders moving towards the "feed everything into buff windows" strategy is pretty much inevitable in any MMO. No doubt the job team simply sees it as simplifying the process by locking everything to 2 minutes.
Potential solution: allow players to coordinate and align their buff windows automatically, with built in flexibility, and let Phys Ranged control it.

(shitty mockup I made, donut steal)
So say BRD, DNC and MCH all get an ability, let's call it Amplify. When they use it, this activates a 15-second timer, during which any of the existing 2-minute buffs get fed into the Phys Ranged's Job Gauge instead of being used immediately. After the 15 seconds, or whenever the user presses the button again, all the buffs go off at the same time, with an extra buff to boot.
This does a few things:
1. simplifies buff alignment which makes parsetrannies seethe because "everyone pressing a single button every 2 minutes is part of the skill!"
2. gives phys. ranged a much needed role in combat by dictating the burst window, which is arguably more engaging than everyone pressing one button at the same time like clockwork, but most importantly,
3. adds flexibility to every class's rotation, because if their burst window drifts, the party-wide burst can be delayed for up to 15 seconds until everyone's properly aligned.
Flexibility is most important because it means drift is less of an issue, which in theory means jobs don't need to follow the 2-minutes as strictly. This in itself doesn't fix job design, but it opens the door to options a little broader than "add more finishers". The other half of the fix is to give DPS and tanks more globals that are situational instead of being "press every time, in this order." Heals, defensives, maybe even movement options should be global, a potency loss in exchange for survival, which in turn gives healers more reason to exist; a good healer is saving potency. And the expectation of wasted globals is built into overall combat design by the new flexibility (extremely optimistic, but let me dream.)
My point is, if everyone has to follow a burst window meta, then give us built-in tools to control it. This is the simplest way I can think of to reintroduce flexible rotations without tearing down what's already there.