That Overton window has come a long way since.
Once the very notion of an ‘OTK’ was a big taboo in this game (see, for example: The game needs more 'disruption', OTKs and solitaires , Cockroach OTK Shaman is back...again - #106 by SparkyElf-2852 … Btw, incidentally, the second topic is precisely about the deck you describe, which that ‘Altair’ guy also mentioned), and the design goal was to make it impossible. Then it gradually shifted to ‘technically possible, but tough to pull off’, and subsequently, it became so that YouTube is rife with videos like ‘Wild Big Priest Turn 1 OTK Sire Denathrius OVER 9000 DAMAGE!!!11111’ (‘too slow’ by modern standards, btw).
This pertain not only to OTK’s, by the way — see the first linked topic.
Your memory seems to fail you, provided you had the right knowledge in the first place. Most often Druids had 14 damage from an empty board (Force of Nature + Savage Roar), more with an Innervate (2 mana) and second Roar, 22 in total, but you wouldn’t see it that often.
The closest was either the Leeroy combo (Shadowstep, Cold Blood etc) from the yolo nobrain faceroll Rogue or the clownish Worgen Warrior deck, the latter probably reaching 30 even (can’t be bothered to count right now), although that deck was generally terrible for playing with, not making Trolden videos or something like it, while the former was quite popular, particularly the greedy version with the goblen, which plebs liked to netdeck for some reason — probably because it played itself for them. By the way, the true aggro Rogue with Coldlight Oracles and other stuff (including Leeroy and other cards, but it generally wasn’t about greedy almost-OTK combos, even though it could technically pull it off, and mostly focused on burning the opponent down) was actually fun and interesting to play with, requiring skill and some thought, unlike practically all other aggro decks (SMOrc, yep), so even I deigned to play it, but overall it was mostly a deck for the elite. 
Are we talking about Standard in particular? Not all of us do. 
When it comes to the crazy stuff — I don’t. There used to be Classic (nostalgia factor, if nothing else, and it was not a bad game back then), there’s been my ‘chillout’ mode — Mercenaries (I suppose that’s a direct answer to you question, by the way), although I haven’t been playing it that much lately, there are occasional Tavern brawls and other content — that’s about it for me.
I’m not a Battlegrounds player or fan, although it’s apparently very popular, perhaps more so than HS itself, so I can’t anwser about it.
The real quiestion is whether they play the game or the game plays them.
See also, for example: Hate this game and hate playing it - #3 by SparkyElf-2852 .
So, apparently this one doesn’t even enjoy the game, but plays the role of a pro-company white knight and troll anyway. Bravo.