I suspect the main reason why is balancing and post-release reception.
ARMS as an IP is built on and based around the idea of the playable characters fighting with really, really long, well, limbs. Like a certain Street Fighter character - Dhalsim - but with the stretchy arms being even more central than Dhalsim's stretchy limbs. This works in ARMS since everyone there has Dhalsim limbs... but not so in Smash.
This creates a major balancing act: it inherently means that an opponent approaching the ARMS character has to guess right once or twice in order to even approach the ARMS character. That's in neutral, where neither character has taken a hit. If the ARMS character lands a hit the opponent oftentimes has to go back to the drawing board. And that is the ARMS character guessing right once.
However, unlike Dhalsim - who tends to struggle up close - Smash's zoners generally also have fast escape / out of shield options. For example, Samus' Screw Attack comes out in 6 frames (1/10th of a second) - no human can react to it - the attack has to be anticipated. Link's Spin Attack is just one frame slower than Samus', but kills pretty early if the strong hit connects. Human reaction times are generally 1/6th of a second for sound (10 frames) and 1/4th of a second for sight (15 frames). That does not count the 5 frame buffer, nor online.
Most attacks in Smash are so fast that people looking to shield will oftentimes do so preemptively.
Min Min also has this quick option - her Up Smash is currently at 8 frames, the same as Fox's (and pre-nerf it was one frame faster). That's her strongest kick. Oh and it has a reflector, meaning Min Min also has a quick answer for opponents trying to zone her back. Even if an opponent successfully approaches her (or a lot of zoners) it doesn't mean the approacher gains the advantage. Sure, she - like Link and Samus above - have a lot of endlag, but the start-up is what matters here.
Aaand I didn't mention the fact that the ARMS' long reach also ensure that ledge / off stage scenarios are a pain in the ass for a lot of opponents to deal with at minimum.
In FFAs an ARMS character may not be so inherently potent because FFAs have 2 or more opponents - that said, FFAs oftentimes have one or two players that try to zone / play defensive - whether it is to keep the lead as long as possible, stall for a KO opportunity, or just to fool around. Also, a lot of casual players have trouble dealing with projectiles or other zoning tools. That means that an ARMS character can also become an issue in casual environments - especially since the ARMS playing style might not be considered as exciting as say Falcon's or DK's by a lot of people.
With the above, it becomes imperative to make sure that the strengths are not overwhelming to the point of intense frustration (for casual or more seriously-inclined folks) and that the weaknesses are there still. They decided to go with Min Min being very vurnerable once she's hit / in disadvantage, very poor airspeed meaning she's prone to being juggled, and a recovery that can be intercepted / hit out of.
That said, by releasing the ARMS character first out of FP2 they get the most time possible to listen to feedback and adjust accordingly. I'm pretty sure they'd rather want to avoid a
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scenario where two late comers prove so contentious / potentially overwhelming that the conversation starts to centre around those characters. Sm4sh's Bayo saw two patches post-release, Min Min has already seen four (five if you count Small Battlefield). It's also a rwason why I'm hoping that they go with at least three post-CP11 balance patches.
And considering how the reaction has been (especially in Japan, but also amongst quite a few Westerners)... yeah the reaction has reached Sakurai and co's ears. There's been quite a few minor nerfs handed out to try and make her strengths a bit less overwhelming and her weaknesses a bit more defined. They're evidently trying to keep her strengths intact (as they would try to with any ARMS character - they don't want Min Min to be especially weak, that'd defeat the point).
Yes, most of the other FP2 characters also break the mold, but they don't have the sheer range (and thus potentially a massive advantage over most of the cast) that the ARMS provide. Sephiroth's Masamune comes kinda close, but even then it's shorter and he was released after Min Min has been out for 5ish months. Meaning that they had a kinda sorta "blueprint" for Sephiroth.
