In terms of buttons, our baseline rotation has technically 3, Demon’s Bite, Chaos Strike, and Eye Beam, but Eye Beam is on a 30s CD, so the majority of our time is spend spamming two of them. All of the dominant talent builds have at least 5, however (the Demonic build adds in Blade Dance via First Blood, and Immo Aura. The Demon Blades build removes Demon’s Bite, but adds in Fel Blade, Throw Glaive, Blade Dance (First Blood), and if running Momentum, Fel Rush and Vengeful Retreat).
That said, even with talents, our rotation lacks much in the way of RNG variance, interaction, or dynamics. The only real “complexity” to be found is ensuring you cast Blade Dance on cooldown (it’s a huge part of optimizing Havoc), maximizing your damage output during the 8s Demonic window (you need to get at least 2 Blade Dance casts off, and with enough haste, 3, as Meta buffs Blade Dance substantially more than it does Chaos Strike), and if playing Demonic Appetite, ensuring you’re not wasting fury generation or cooldown reduction from soul spawns.
In terms of number of buttons, the most basic one is Arcane. They rotationally use Arcane Blast spam, weave in Arcane Missiles every few GCDs as Clearcasting procs, and occasionally drop their charges via Arcane Barrage (how often they do this depends on their build, mana level, and gear). During their burst phase, however, Arcane Barrage is not used, reducing it to only two buttons.
That said, Arcane actually requires attention paid to mana, and judgement calls on when charges should be dumped and when they should be retained. The entire rotation is about balancing mana costs versus damage bonuses, and thus isn’t really that “simple”.
Beast Mastery has a fairly simple rotation as well. They only use 3-4 buttons, depending on build: Kill Command, Cobra Shot, Barbed Shot, and if taken, Chimera Shot (which has fallen out of favor over the last tier or so). In BfA at least, BM largely doesn’t have to pay attention to focus, and they cast Barbed Shot exclusively for the buff, not for the focus restoration effect. Their only real complexity is ensuring Kill Command is cast on cooldown, and aiming to cast Barbed Shot as close to it expiring as possible, to give the highest uptime on the buff at 3 stacks as they can. The dominant build, Dance of Death, makes this much easier, however, by substantially increases the chance of regaining a Barbed Shot charge on an auto-shot crit (combined with stacking a boatload of crit chance).
On the other end, Affliction with 8 rotational buttons in the dominant single target build: Agony, Corruption, Siphon Life, Unstable Affliction, Shadow Bolt, Haunt, Phantom Singularity, and Deathbolt. However, their rotation is honestly rather boring, as it can easily be described as “refresh all of your DoTs if they are below 30% duration remaining, use Haunt, Phantom Singularity, and Deathbolt on cooldown, and spam Shadow Bolt if you have nothing better to do”. The only real depth to it is refreshing your DoTs and dumping shards into UAs every 30s for Deathbolt, and otherwise aiming for high UA uptime due to its 10% damage bonus while active. Most warlocks I know kinda hate Aff’s rotation, though fortunately it sounds like it’s changing pretty considerably in Shadowlands.
Feral has only 5 rotational buttons (Shred, Rake, Rip, Ferocious Bite, Tiger’s Fury), same as us, but their rotation arguably has some of the most complexity to it due to the snapshoting mechanic on Tiger’s Fury’s damage buff (bleeds applied while it is active retain the damage bonus for the duration of the bleed, unlike nearly every other damage buff in the game). Add in complexity-increasing effects like the Blood Talons talent (requiring them to weave in Regrowth casts at specific times to buff their damage further) and Wild Fleshrending (adding Thrash to the primary rotation), and theirs is a highly complex DPS rotation, despite the number of buttons.
Anyway, longwinded way to say, number of buttons isn’t really a good indicator of rotational complexity. Affliction has more than Feral, but Feral is wildly more complex. Arcane has fewer than Havoc or BM, but Arcane is rather more complex than either.
If anything, they’re likely to continue dumbing it down. They did just announce official support for console controllers, after all, and you can’t have too many rotational buttons if you’re going to be able to do them on controllers.