I'd think that most people who eat with their mouths open have enough experience with it that they don't spill, which negates two of your points.
I question whether those who eat with their mouths open are self-aware enough to train such an ability in the first place.
1: Not having to swallow before saying something. Which might be something important, like "lion!". I've seen people choke because they attempted to swallow unchewed food so they could answer a waiter.
I fail to see how chewing with a closed mouth precludes opening it in such dire emergencies. And the waiter who deliberately asks questions while people are chewing might, on inspecting their tip-jar, like to speculate on how much they've lost due to such irritating behaviour.
If there's any connection between the act of liquefying your food before swallowing and open vs. closed mouth chewing, frankly I can much more easily see how open-mouthers are more likely to choke, since those with closed mouths can complete the mastication process to its fullest extent with no fear of anything accidentally "leaking out" of their gaping, anti-social pie-holes.
2: Practice for cunnilingus.
You eat at your mothers table with that idea in your head? Cunnilingus is practice for cunnilingus.
3: Being able to chew on what's too big for single bites. Like gnawing on bones.
Gnawing on something too big to put in your mouth, and therefore chew and swallow, is not what is being talked about, and needless to say the sound output is different.
The biggest downside to eating with an open mouth is likely etiquette. Which is important enough - it's the grease in the machinery of interpersonal relations.
It's true that there is a lot of arbitrary etiquette around, but some of it has sanitary origins too, and I think eating with your mouth-closed is one of those things.