I guess it could work either way. I mean, Nagini could be obeying Voldemort by virtue of being a well-trained pet, the Basilisk for... whatever reasons the Basilisk does anything for, and Malfoy's summoned snake might listen to Harry because it's inclined to grant random non-difficult favors when asked. None of those seem any less probable than snakes winking, talking, having theory of mind, speaking in ridiculous hisses or knowing Spanish. In fact, none of the snakes in this series seem like snakes at all, so I'm not sure what my priors are regarding them.
Parseltongue speakers don't just talk with snakes, they command them.
Do they really? The boa constrictor seemed pretty interested in its own stuff, Nagini is a pet and pets in general are obedient, Harry didn't command the Basilisk... so is this actually canon? Admittedly, maybe I just missed something, but I don't remember this.
What if the problem isn't that it's too cognitively taxing, but that, applied in the sloppy way most people apply their heuristics, it could lead to irrational choices or selfish behavior?
...Doesn't everyone already believe #4?