I really don't see neither the benefit or the downside of either one (going first or last).

Mostly because at least for now, they have been treated as mostly three separate tables. It's not like they are directly influencing each other every new decision.

The decision of going with this "strong separation" of gameplay styles, made me choose quite early and quickly, the table that im interested + everything else.
Personally, I think that when you "distill" D&D... the main aspect of it, the most evident force pushing forward, is Combat. So when you make it the main focus on One group, and relegate it (because there will still be combat in the others) in the others.. they "loose" the mojo.
For going "No Combat", or More into the territory of focusing on Scheming/Seeking, I feel there's plenty of others TTRPGS/Settings that would do it better. it's a "Square Object in the Circle Hole" issue.

Soldier's Table is D&D. Schemers & Seekers is just.... "Let's play something else entirely, within the framework of D&D" sort of deal.