Exhaust balance pipe - why?

So what exactly what is the function of the balance pipe or collector box
between the pipes on a twin exhaust? What difference would it make if each
cylinder just had its own independent exhaust pipe and silencer?

 

Exhausts are all about pressure waves (aka as sound). As the
waves travel around in the plumbing they cause low pressure
and high pressure zones at varying places at varying times.

The ideal exhaust system would be one that cooperated
perfectly with the desired flow at the exhaust valve, sucking
most of the time the valve is open but maybe even stopping
the flow at just the right moment, at certain revs, to stop
fresh air-fuel mix escaping down the drain.

The pressure waves bounce where the pipes change diameter
or ends. By arranging a number of diameter changes, pipe
ends, baffles and chambers (of exactly the right volume) at
exactly the right distance from the exhaust valve it is
possible to tune the system to improve one or more engine
characteristics.
Using balance pipes gives the tuner pressure pulses that
start out of phase with the cylinder he works on and those
can be put to good use. They can replace ridiculously short
or long systems. BMW even had two crossover pipes on some
boxer model (/5 and /6 ???).

Of course there must be a slight effect on gas flow
resistance as well and a chance for a multiple damper system
to sort of share the load.

Or something like that.