Punching through the ITCZ is not a habit to be recommended, serviceable pitots or not. I have done it several times and it is one of the worst flying experiences you can have. The Captain would have known that.
We will never know why they did not deviate 100, 200 or 300 miles to go around it. It is plausable the 1st and 2nd officers did not feel they had that sort of authority and did not want to wake the old man up for his say so. I think it was a grave mistake of the Captain not to have been there and the talk of him needing rest so as to be rested for the approach is laughable, there was another 7 hours for him to sleep after the ITCZ.
My guess is the plane would have deviated if he had been there. I mentioned at the vey beginning that I suspected the Captain not to be in the cockpit and was shouted down by the experts.
IMO it raises other issues of whether the younger generation of pilots are too hestitant to do things without a clearance. Did they ask for a deviation? Perhaps they did and could not get through or it was denied? Descend 500 feet and deviate anyway without a clearance but I think this sort of thinking outside the box is not encouraged in pilots anymore.