Now that any class can unlock any armor what do you consider the best class for this? Are there still raid boss mechanics that require a pet also?
I thought druid since it’s super fast, it can go stealth, it can port out and is super tanky bear, but has no pet…
warlocks or hunters really
Any class can solo anything upto and including BFA.
With that said, a druid with dreamwalk can be handy, especially for dungeons. Hunters are also naturally speedy, which is nice.
hunter with empty bags 
why does a pet matter?
I feel like you’re thinking about this too much, druid has always been the answer, and then after that if you prefer something else that also has high mobility
I would say a Demon hunter with a speed set and tons of mastery. Other than that, I would make sure it has access to increased speed, like a Shaman for ghost wolf, or druid for cat/travel form… along with a speed set haha
Hear me out. Fury warrior. All you have to do is spec to make your aoe free. Then you just run around spamming your free aoe.
I dont know, i was asking if some boss mechanic requires pet, or if everything is really soloable without
Druid and you’re good to go, homie! If you really don’t like druid spec as mobile as you can on your most mobile char 
Anyone with lots of cheap AoE. A constantly spinning Windwalker monk for instance.
Druid with a speed set.
Outlaw Rogue is specifically better for farming Razorfen Kraul.
Druids have a full tool kit. Some of the best speed, the best AOE, shadowmeld to disengage combat if nightelf, reduced fall damage in Kitty, instant travel forms including aquatic, and a portal to quickly get back to a dungeon entrance. I only farm Druid these days.
If you pick any of these other classes for nothing but AOE you’re missing out.
Only Night Elf Druids can Shadowmeld. However, Feral Druids of any race can use Incarnation and then Prowl for the same effect.
To be clear, it’s not “any armor”. If it says “Class: warrior” on it you have to be a Warrior. Why Blizzard carved out this exception under the guise of “class fantasy” when armor set tokens are Warbound is a mystery.
BM Hunter. Instant cast ranged AE with no CD (Multi-shot), natural speed and a pet for some mechanics but also more difficult bosses, usually from the previous expansion. Plus you can send your pet to kill something while you simply keep running.
Also, don’t underestimate Feign Death. You will find in various old zones that running through a bunch of mobs because there’s no point in stopping to clear them will get you stuck in combat (I’m looking at you, Mechagon)… This is really annoying when it happens. Having the ability to leave combat can be really useful. Even if it’s in a large raid instance where you don’t want to kill everything you’ve aggroed (or, worse, wait for it to get there).
You can make a case for druid as they have stealth (to skip to the end) and can more easily reset a dungeon. Also, as a bear you can pretty much anything from a previous expansion (pre-11.0.2 at least). They don’t do a ton of damage though. Their AEs are generally melee range not ranged and the ranged AE is more limited to use than Multishot. Personally I don’t vibe with how a druid plays. Obviously YMMV here. If you do like it, it might be the best choice.
DH has Speed from Mastery and in some legacy content the double jump and glide will allow you to skip things other people don’t. But no ranged AE kills it for me and so many abilities are on CD (even a short CD) that I find myself juggling whatever ability is up at that time.
Just level all of them in Remix or even from the prepatch event. It’s never been easier to level. May as well take advantage of it and give yourself options.
Also, it’s worth having multiple toons when it comes to farming legacy content. You can park them at certain raids and dungeons or in certain zones rather than wasting all your time travelling. It adds up.
I think hunters, rogues and druids are all naturally speedy. This is also very much worth checking out, but some it can be a lot of work to get:
Making a Dragonflight Speed Gear Set and running Legacy Raids/Dungeons FAST - Wowhead
You want a class that has:
Some good candidates:
WW monk is my favorite due to high speed, insanely high burst (partly due to xuen talent double dipping on legacy damage multiplier), tons of spammable AoE, and good self sustain.
In my personal experience, these classes are fairly slow:
what?! warrior is fine.
Enhance shaman and Outlaw rogue are pretty good, imo. Priest with feather and holy nova is okay too.
I don’t think any classes are bad, warrior just feels like a slower version of WW monk to me.
Beast mastery ftw. Not only can you solo old content, but also newer stuff that is normally impossible to solo (yet) for most classes too. Think Torghast, Delves, rares, previous expansion raids, etc.