The point of ARMS is that, with the ideal control style, you are able to stagger punches and control their movement at the same time. While you might argue that you should be able to control the directions of both punches with both analog sticks, what happens when you punch with a single hand and want to move in another direction? Does movement automatically snap to the "other" control stick? That's needlessly convoluted and unintuitive. Therefore, you become stationary when punching and move your singular punch inputs with a single control stick.
You argue that Splatoon mixes things better, but Splatoon's gyro/control stick mix is used to control the camera alone, not two separate types of inputs that can occur at the same time. I think that's an unfair comparison to make, especially since ARMS doesn't have camera control. Your disappointment regarding the lack of trigger/bumper usage, I can understand, but your motion and gyro argument doesn't make sense to me.
And while I enjoy the competitive fight game angle of ARMS, judging by the lukewarm reception from the majority of users on this site and your accurate description of the importance of precision in fighting games already invalidates the chance that this game will develop a strong FGC following. Except, thumbs-up grip offers more options and precision than traditional controls do, which is simultaneously the reason the game could be an outstanding example of traditional v motion control, and also the reason it could fail to garner any sort of eSports presence in the same way Splatoon failed despite having similarly solid foundations. I can't think of a fighting game that DOES offer higher precision with motion controls, so arguing that precision is favored by competitive players simply isn't true. Many competitive esports do require motion inputs at professional levels, so again, saying the fighting game community is going to make or break this game is absurd, partially because the argument is fruitless anyway since ARMS isn't looking like a major seller anyway, and partially because the people who do seem committed to playing it at a high level are favoring the motion controls anyway.