Cooldown reduction is tricky in a setting like FFXIV. Let's say lilies could reliably reduce the cooldown of certain actions by 50%. If we're talking about a healing resource like Tetragrammaton, that means we're taking a 60 second cooldown down to 30 seconds, but unless you use Tetra immediately, every second you're sitting on it after the 30 second cooldown is rapidly declining the value of the cooldown reduction effect. And if you end up not using Tetragrammaton for 60 seconds or longer, the cooldown reduction became entirely useless. And that's a problem with having cooldown reduction on exclusively recovery tools. It worked with Aetherflow because you use Aetherflow on cooldown and could spend excess Aetherflow on Energy Drain, so a good Scholar player wasn't wasting resources while still taking advantage of the full CDR they benefitted from.

If we translate this to an attack action, even with the 2 minute meta, there are things you can do to make CDR work. For example, when I mentioned Tetragrammaton, I mentioned a hypothetical where we take a 60 second cooldown down to a 30 second one. If we have a tool that is usable on cooldown at all times, such as a damage tool, then you can work within values that align with 2 minute windows. 60 seconds > 30 seconds. 40 seconds > 20 seconds. 30 seconds > 15 seconds. 20 seconds > 10 seconds. All these do work within the 2 minute meta since you'll still have that resource available at the 2 minute mark.

That said, we don't need to talk as if the 2 minute meta is permanent. Just because nothing has been don't about it through all of EW doesn't mean it'll never change. I'm not going to try and sell the idea that it will absolutely be abolished in 7.0 or anything, but given how they approach major changes in this game, it makes perfect sense that even if they were planning to change it, that we wouldn't see anything until the next expansion anyway. The balance of EW has been built around it, and you'd need to make very drastic changes to break away into something else--the level of change you'd normally encounter during a new expansion.