I’m one of those weirdos that prefer slow and deliberate combat and I don’t like spamming clicks for the sake of my wrist (yes oldschool Paladin was my favourite class, relaxing auto-attacks!)
With the Haste stat I’m forced to click faster and more often so I avoid the stat. Which classes function optimally with only Vers, Mastery and Crit?
I can take naps in between button presses on my current Retribution Paladin if it helps.
(I’m kidding but the Ret Pally may be what you’re looking for)
Ret Paladin,
Elemental Shaman,
possible Rogue comes to mind…
I found auto attacking to be really satisfying in Classic, especially big crits with two handers.
Yes, I wish Blizz still designed Pallies around Seals… it was a great option for us who loved chunky auto-attack slaps.
I honestly feel like Seals+Judgments would help round out the ret paladin rotation right now. You could even reduce haste’s impact on our rotation to account for the new fillers.
Plus, class fantasy.
You might want to play a caster. Destro lock is very slow and relaxing due to our cast times.
Chaos Bolt is always a satisfying button too, regardless of Haste.
White damage was a important part of a dps’s morning breakfast.
Do not suggest Ret. Ret is absolutely awful without haste.
Unless OP doesnt want to do high end content or just doing N raids or stuff like that. Ret with no haste is the most awful, clunky, inefficient thing I can imagine.
May I recommend an Arcane Mage?
Arcane is all about managing mana, so haste isn’t a great thing because it can lead to depleting mana too fast.
And there’s something satisfying about slow but solid arcane blasts taking chunks out of mobs. 
Mages, Unholy Death Knights, Boomkins, Affliction Warlocks… These have something to say about no-haste Ret being the most awful.
Marksman gets silly with low haste; you’re aimed shots are slower then continental drift but the damage you can crank of of them with double tap and some decent crit means you can often times knock out big chunks of your opponents health in short order and this gets even stupider with the aimed shot:multishot loop if you’re dealing with packs.
Further, you can get some formidable AOE’s going with just a few talents; explosive shot is solid for Mythics and Volley is good for all kinds of situations.
I dont play casters. But I definitely can see how that is awful as well.
WW Monk.
That class has historically AVOIDED the stat.
Survival hunters
Rogue. Sub rogue you just want verse and crit. Things die too fast before we go tired
This. You can basically avoid haste if you want as WW (generally just keep it around 5% or so).
what also sucks is running 4 mythics and walking away with nothing. freaking hate this game and i hate personal loot