One drop design is this interesting thing. It's really awkward to design them right. The thing is that in the agnostic game "mana efficiency game" the abstract concept of, what if i built a deck with 1s, 2s, 3s, etc, how would I maximize my chance of spending all my mana every turn with minimal use of hero power to do that, in that minigame, one drops blow. They blow at that in Magic too, and they blow even harder in Hearthstone. So if you want to entice people to actually play one drops, you either need to give them the busted warlock hero power, where the mana efficiency game is trivially easy using any deck and just activating hero power the appropriate amount of times, or you need to hand out one drops that give so much meaning to being 1 pt. ahead on your mana efficiency early on that they are insane. Which means you basically need to make them as powerful as two drops, but then print 1 on their mana cost and pretend its ok. It's a lot easier to get away with that if it's Mana Wyrm and class restricted. Anything neutral is gonna become pervasive.
You really don't need turn 1 one mana creatures to make a good card game, even though Blizzard seems to think so. Playable one drops are inherently swingy since they provide you some tempo in the first three turns, but do nothing if you draw them later on. If they're not in your opening hand, they don't offer anything to the mana efficiency minigame. 1 drops like Earth shock and abusive sarge are different, of course, those are good.
I've watched zoo mirrors in modern in mtg, which revolves around 2 mana quality 1 drops duking it out. I haven't ever found it particularly fascinating.
I think it'd be a good plan to keep all neutral 1 drop turn one plays at about leper gnome power level where only warlock is interested in them, and let the other eight classes design strategies around turns 2-10 instead of printing stuff like undertaker that forces people to play that one drop just because it's a 2 drop.
I don't think undertaker is currently that pervasive. It's in the best hunter deck, and the second best warlock deck (which plays tons of 1-drops anyway). Then there's decks that try to squeeze the deathrattle theme with the mech theme thanks to the good deathrattle mechs, none of which are particularly spectacular. And there's undertaker priest which I guess a couple of people play... Zombie chow is similarly popular because it's actually the value of a 2-drop.
Anyway, I like undertaker because I like things that threaten to grow or make other things grow, because that messes with the calculus of what is worth killing. Do I coin my dark bomb or play zombie chow? Depends on how likely he is to have 2 1 mana deathrattle minions. I do get that it's too strong for a 1 drop though. If your opponent gets 2 early, there's almost nothing you can do. That makes it swingy. I don't think it's useless late game though since it can still grow, so it's not really swingy in the way you describe. Zombie chow is swingy in that way.
All in all it seems your arguments suggest zombie chow is a problem card. But I guess it escapes because it's a 1 drop that's not good for aggro, so those swings don't end the game as quickly...
Zombie Chow is a pretty crazy card. But undertaker is, I'm 1 pt. ahead on the mana efficiency game, and now I'm melting your face before I run out of cards in hand and start failing at it. Zombie chow is, I'm 1 pt. ahead on the mana efficiency game, but I'm gonna make us play it longer so that I have a chance to start failing at it. So only Warlock is really able to use it in a compelling way, and it's probably only going to show up in control decks with really good draw mechanics otherwise. Priest has pretty decent draw and can draw even better when it has 2/3s bopping around so that's another one.
If Zombie Chow's mechanic showed up on a card that put more value in hand like Pit Lord it would be way stronger. What keeps Zombie Chow within reason is that a control deck isn't excluding Crocolisk because Crocolisk isn't worth 2 mana, a control deck is excluding Crocolisk because Crocolisk isn't worth a card.
I think the undertaker nerf is offputting because DBoom is definitely stronger and midrange and control feel like they need more of a look, but I do think undertaker was probably not great for the long term health of the game. Playing Frostbolt on a 1/2, and feeling like that was definitely the correct play, and feeling like it was correct, within the meta, for my deck's gameplan with respect to undertaker to be to trade down, was a tipoff that made me feel like something's the matter with that fellow. It's bad when cards have a "beat the rest of the deck" feel to them like that, where it's optimal to design your deck to just take a bad trade with a card when you see it and then try to make good trades with the other stuff that's in there. Most classes didn't have a good trade available.
Maybe if we're lucky we will see some deck that is held back by the strength of undertaker come out and shake up the meta. I for one am excited to play my Mech priest more, since I have unexpectedly good results with it, and it doesn't use undertaker or undertaker hate.