But then Zandalari move faster while you're
not stealthed, which is every time you're fighting. Also, druid stealth has a painfully long cooldown, which you will feel even more if your highest speed is linked to it. Personally, I can't stealth from pack to pack when clearing old dungeons/raids with trash included, but maybe you know something I don't. For me, this scale would only ever tip towards NElf if I'm doing bosses only, but then Ghost Wolf is overall faster than any cat, and Zandalari can be shaman too.
As to the original question: levels that can unlock azerite traits can
potentially be faster than a 10/20. Imagine the same stuff, but then you can stack
Longstrider on top of it. And then levels with a high enough ilvl for
Elusive Blasphemite can also stack that on top of the rest.
Minor Speed is a must.
Alas, the higher you go in levels, the more difficult it becomes to cap tertiary speed, and effective use of Longstrider requires stacking one chosen secondary stat (don't let the tooltip fool you, that cap is not there in practice - at 62.91% haste my 70 mage gets 18% speed per piece for 54% total, although this may get "properly" fixed at some point). Essentially, you're balancing tert speed vs. longstrider secondaries, with 3 major equipment slots not being able to give any of either. You'd want a level with a high disparity between "intended" and obtainable item level.
Sadly, you probably already missed the boat for 70s (especially if you have TWW and are single-account). I'd probably try something like 61, where you can get 357 gear from the AH and see how the TWW enchants scale (+1000 speed on bracers is OP AF at 70). Alternatively, 71 looks interesting, but then you need to be careful not to level without XP off (you get access to some TWW crafted gear and possibly other things like consumables). If you're only doing old content where you get no XP anyway, this may be viable.
In terms of classes, while I would say that druid is the overall cookie-cutter for speed kits, I actually use a combat rogue for outdoors non-aoe farming, and rogue (if there are chests or locked doors) or shaman for boss-only instance clears. Sadly, I can't find an on-demand AoE skill for either, but I haven't checked all the specs in some time. That actually would put them on par or strictly ahead of my druids.
Hope that helps.
EDIT: Oh, it may be worth noting that Longstrider only works up to BfA, so not in SL or DF. But then, 70s don't get legacy loot in those anyway, last I checked. You possibly need a different approach there.