A huge part of the complexity comes from the sheer volume of buttons involved in the “rotation.” The core rotation is 7 abilities. That’s before borrowed power abilities, before talents; it doesn’t include Chain Lightning, though you constantly switch between it and Lightning Bolt at any given moment, and it doesn’t include Feral Spirits because it’s only once every couple minutes. It also doesn’t include maintaining Windfury Totem.
Typical talent setup adds Sundering and another cooldown, plus you get another button from your essence, which, depending on what you have access to, adds either another cooldown or another ability to your core rotation. I believe that makes it 12 total buttons. But most of your time is spent casting those core 7, and you press them a relatively equal number of times.
Elemental Shaman has four buttons in their core rotation: Earth Shock, Flame Shock, Lightning Bolt, and Lava Burst. And maybe count Frost Shock because sometimes you’ll use it to gap-fill while moving. Once you account for talents, cds, and an essence, Ele’s total number of single-target rotation, damage dealing buttons is 11. That includes Earth Elemental, which is a five minute cd and does barely any damage afaik, and it includes Icefury over Primal Elementalist, which adds two buttons (Icefury and Frost Shock). But again, most of time s spent pressing those core 4 buttons.
And that’s a big difference. 12 buttons vs 11 buttons looks much closer than it is. the 7 button vs 4 button comparison is probably more accurate. On top of that, keep in mind that Enh is juggling all these buttons plus paying attention to a dot, and managing an rng combo point system, and reacting to procs. Not to mention interrupting, throwing the occasional off heal, using a free global to drop healing stream totem, or whatever other utility… And, oh yeah, we’re melee so 90% of mechanics are designed to hose us, so we’re frequently moving at the same time.
None of that should be taken as a complaint. Enh is my favorite class/ spec in any game ever (and it’s not close), especially now that we’ve reverted back to the pre-shi**y-energy-bar-and-praying-for-procs version. And I will always come down on the side of people playing what they like, and so don’t look down on Havoc Demon Hunters or Arcane Mages for playing 2 or 3 button specs. But in terms of complexity or difficulty or whatever you want to call it, Ele simply doesn’t come close Enh. And in general ranged dps is nowhere near as hard as melee.
Now, if you want to compare Enh to, say, Outlaw, that would be an interesting debate.