There is no substitute for cubic inch or in this case surface area

...And then some.

https://youtu.be/iGa9259pz-I

How does sound stage and woofer size go together? I thought that is more a characteristic of mids and highs. 

I think of multiple small woofers only in the sense of how HIGH they can go. Given the same volume (moved air), the key to me is that I can run an 8 woofer much higher than a 12", potentially allowing a much simpler 2 way crossover with all the potential negative impacts from any part in the signal path. 

What I don't know is if (given the same air move volume) if four 8 inchers can reach as far down as a 12" (SPL at low frequencies, and resonance frequency). 

Directionality increases with frequency.  Larger midranges will be more directional so placement matters more.  My experience has been that I prefer speakers with a smaller midrange.  They tend to have more even in-room responses.

At face value 12 inch drivers will put out a bigger soundstage than 3 inch drivers.  

@bassbuyer can you explain this please?

Larger drivers should have a greater SPL (sound pressure level).  dB SPL measurement.  Putting out a greater sound volume.  It should sound louder to you. Which you would perceive as a greater or bigger soundstage with well designed and setup speakers.