The risk here - which would happen immediately in my game - is that the louder and-or faster-thinking players would drown out the others, and end up getting three actions to their one unless I put my foot down...and impose a speaking order...which then might as well be an initiative order.Interesting, although I think you still get that naturally when people have to think and react more quickly without a fixed order of turns. I'm not saying it's really a problem, and some people will work better with a structure in place. I just prefer to not have a pre-defined structure. Each group of players seems to work out what works for them in the games I run.
The route to simultaniety is to use a smaller initiative die and allow ties.
The route to not using initiative at all passes, I think, through bedlam.