Apparently also called Bronstein Shuffle (which also sounds like a fun dance)

A key part seems to be alternating turns placing pieces. I wonder if this would result in top level gameplay converging on certain opening placements? If so, I wonder how not taking turns but deciding on placement privately beforehand might affect gameplay.

Anyway, maybe when the pros get sick of Chess960 they'll give this a shot :)

It would be effectively be the opposite of Chess960 -- instead of reducing the impact of studying openings, it would add a whole genre of placement meta you'd need to study to be competitive.