A bit of an essay here, sorry, but once I started thinking about it, my fingers kind of took on a life of their own.
You're right that any character could use the same combination of ranged attack and ranged defense, but I think a Templar might be the only other one that could do it as easily. The Witch's starting point on the Passive Tree gives her quick n' easy access to the damage bonuses for Fireball and upgrades for her minions, and she doesn't have to spend any Passive Points seeking out Intelligence bonuses. The other Basic Classes would have to expend Passive Points working their way around the web. The Marauder has some Fire passives, but several of them - Magmatic Strikes, for example - apply to Fire Attacks, not Spells, and so wouldn't improve the damage of Fireball. I'm not sure whether Passive Skills that "convert % Physical Damage to Fire Damage" would apply to Fireball; if not, then many of the Chieftain's passive Fire skills wouldn't work. I think a Templar could make use of Zombies well enough - in fact, it's real easy to get carried away and accidentally cripple your Templar by making his Minions
too good, trust me

- but I think only the Elementalist can have 4 Elementals.
So I think the issue mainly lies in the combination of ranged offense and ranged defense that Fireballs, Zombies and Elementals provide, and the Witch is particularly well-positioned to leverage that combination. It may be that (a) another combination of Skill Gems and equipment that I haven't thought of provides an equivalent balance, or (b) the extra Passive Points another Basic Class would use to upgrade their Fireballs and Minions is offset by easier access to a pivotal node nearby their starting position on the skill web. Taking a quick glance around the outer ring of the web: Point Blank and/or Long Shot, set between the Duelist and Ranger, look like they'd be great for Fireballs. I'd have to see whether it's more efficient to start from the Witch and use up a lot of Passive Points getting one or both of those, or to start with a Duelist or a Ranger and then use more Passive Points to get upgrades for the Fireballs and Zombies. I would assume it's the former, but I haven't done the math.
A third possibility is that this Witch has a critical weakness I just haven't stumbled onto yet, that will seriously limit her progression through the Atlas. Most characters can sail through the Acts, so something like the first 70 levels of any character aren't an awesome measure of her capabilities. On only the second tier of Atlas maps, I did get into a fight that killed all of my Minions, and forced me to scramble a bit to defeat the last Boss without getting killed. That had never happened before. iirc, my Zombies have 5000 health and my elementals have 9000 health. So that would be a fast 136,000 points of damage to kill them all - if it was from directed attacks. It probably wasn't, though, it was probably a lot of AoEs. 10,000 damage from wide-area AoEs could kill all of her Minions simultaneously.
However, ime, in any game where you assemble your capabilities from an array of options, and/or have to use your capabilities in a particular way to leverage your strengths and minimize your opponent's, there are two measures that I think of as the "floor" and the "ceiling." imo, any evaluation of a build or character needs to take those measures into account. In simplest terms, how easy and/or intuitive is it to make a build that's capable and/or utilize your chosen avatar's inherent capabilities, and how powerful can that build or avatar eventually become? Most of the time, the 'floor' doesn't matter a lot to experienced players and the 'ceiling' doesn't matter a lot to newer players. With the two versions of Witch that I've played, the 'floor' was very low: The builds seemed to fall into place almost by themselves, and there wasn't anything tricky about using them effectively. I don't think I did anything particularly clever with either of them. However, I haven't played either one into the later stages of the Atlas of Worlds, so I'm not sure what their "ceiling" is. I think my Necromancer got about halfway through the Atlas, and my Elementalist has only just started. It's possible neither one can reach the heights required to complete the tougher maps.
Oh, one other thing: I've found that both Witch builds aren't awesome in the Delve mine. Of course you can choose the level of enemy you face, and you don't
have to go down there at all, so it's hardly a crippling weakness. But I do want to try going really far down there someday. I don't think I've gone much past Level 70, and I get the impression that a purpose-built character may be necessary to reach, like, Level 1000 or something. While I was playing last night, I noticed somebody had reached Level 10,000. I wouldn't be shocked if they have a dedicated, deep-dive character and a whole different character for farming Sulphite in the Atlas maps.