The complication here is that the simple relationship between wight (or downforce assisted equivalent) coefficient of friction and traction is only true up to a point and in performance tyre that point is where the thermal and mechanical loads on a tyre start to change its mechanical properties.
Performance tyres are generally designed to work best with a small amount of slip angle ie just at the point where static friction transitions to sliding friction so in an F1 context the contact patch of the tyre very much does make a difference. In this context the 'grip' is effectively the maximum load a tyre can tolerate before it transitions from static (rolling) friction) to sliding friction.
This is not so much about the 'classical' theory of static friction as that ability of the tyre compound to deal with the amount of energy being put into it.
The 6 wheeled car was not so much about the fact that 4 drive wheels are better than two but a clever exploitation of the regulations which limited rear tyre size but neglected to specify that you could only have two axles, something witch was very quickly changed.
Note also that the 2017 F1 regulations increase the width of the tyres for the explicit reason of increasing performance.
In summary while a larger tyre contact patch does not increase grip/traction in general it very much does increase the upper limit of grip where the limiting factor is the breakdown of the tyre compound.