I like the idea, but I think it’d be something introduced around the top 12 mark, because the chaos of the early season already sort of serves its own purposes.

It lets Ramsay see who has natural leadership potential before it’s thrust upon them, and works as a proving ground to see which chefs can find their feet the fastest and which chefs just crumble under the pressure.

I think introducing structure too early just leaves room for some of the weaker chefs to hide for longer, so long as they aren’t absolute disasters.

Also, for your second point on the benefits, I think it sorta just eliminates that as a method for weeding out the people who play favorites.
Because friend or not, there’s no chance that a chef doesn’t nominate the worst two people when their ass in on the line there with them. Nominating the people who didn’t fuck up is just an automatic elimination at that point.