While many customs are indeed rooted in logic and this one might very well be too, it's not due to the customs you've listed.

Food spreads disease and infection when it's not done correctly and especially in that sense doing it together would be counterintuitive because that way if one persons eats it and gets sick everyone would because you share. Food can also be stolen, poisoned and is easily modified. (Sticking with the primitive here).

Where as defecating arguably puts the person in a vulnerable state, it does not spread infection unless you roll around in it or eat it.

The reason we, humans, eat together is indeed primitive: we share. We used to be hunters and gatherers and food wasn't always around. So to make sure distribution happened accordingly it was done in a group.

I think the modern pooping habits have to do with "modern" vanity. It smells and you have to expose a part of yourself the modern human is used to generally hiding. Further proof of the silliness of modern poop-habits is the well-known phrase: "Pretty girls don't poop". Of course they do, but it is something people, guys in particular, rather not think of, let alone want to witness.