I doubt your conclusion that unified action needs unified mentation. One may take unified action without achieving unity of the contents of the brain. Acting with instantaneous regret if you will, flying by the seat of your pants, etc. The brain seems to be able to let competing subsystems alternate getting expressed in action.

Can you state in plain terms what this actually means?

> There is no way to allow each limb to do its own thing, or the brain not to decide what comes next in a unified way.

This is of course not true. I’ve watched people trip over their own feet because the simultaneously tried to go both left and right. I’ve done it myself.

And this says nothing about consciousness. Most actions are not conscious.

There is no way to allow each limb to do its own thing

What? Why not?

It's physically possible in terms of limb motion. It's very difficult for most people to actually do, sure; but impossible?

or the brain not to decide what comes next in a unified way

There's the idea that a lot of the brain's "conscious decisions" are actually post-hoc rationalisations of unconscious decisions. If so, there's no reason those decisions have to be unified. Maybe the consciousness of the decision and its outcomes must be unified; maybe that's somehow connected to what consciousness really is. Or maybe not!

I don't think there's enough information to say.

> There is no way to allow each limb to do its own thing

I can pat my head and rub my belly at the same time.

If we're talking about consciousness then yes you can walk left/right at the same time. You can drink coffee before it's brewed.