Not quite, using Valigarmanda EX as an example, for the donut/cone/out tell, it only shows up the first time it's done in the fight, and then doesn't even show up in the text channel afterwards. But that's not a universal thing, because both volcanic eruptions + all three avalanches get the DBM-alert text onscreen(+in chat) each time they show up.
But even if that was the case, a lot of these mechs they use the text for only show up once or twice in a fight anyway, so it'd still be happening like half the time. Maybe if they turned them off if you'd already cleared a fight or something, it'd be a bit better/less intrusive, but then I could see people complaining about fights getting harder after they'd cleared it once (which I would be okay with, tbh).