I do think this plan is weird and poorly thought out from the writers' perspective. The question you're asking is a good one. As far as the impact of the plan on the dead three, I think there's a somewhat reasonable explanation for that at least. Firstly, they can probably spare their worshippers. Secondly, the dead three are no longer full gods at this point, so maybe the idea is that they're less reliant on souls? I could see a scenario where their plan works and brings all the gods to their level, and the dead three end up with the advantage because they're more used to this level of power and can get the drop on their rivals. That would make sense to me.
But this plan with that goal seems weird and illogical to me for other reasons. Chiefly this; I'm not familiar with the setting, but there are more places than just the sword coast, yes? I presume that the world is a WORLD, with multiple countries and continents. So I feel like even getting rid of the souls in this one admittedly densely populated area wouldn't be that damaging if you're working on a global scale. This plan would require them spreading across the world to work, I feel like. And that seems kind of absurd based ono what we see. This issue feeds into another problem I have with the plot of this game; the scale of its consequences are all over the place. It can't seem to decide if it's about the fate of multiple planes, or just this one important city. I don't buy that just ruling this one city is going to have multi-planar consequences. Especially since I don't feel the game does a good job of explaining why the city is so special and important. I get that it's a major trade hub, that's good enough. I buy it's a major power in the region but the game doesn't really sell that. Mainly because it feels so isolated. I never feel like the city influences the wider world because it doesn't really feel like there's a wider world to influence.