That is why BR were stupid, it is a well known fact that even many years ago if you travelled to Manchester either by the A57 Snake Pass or the A628 Woodhead Route you would get stuck at Mottram Moor for ages and people wanted to go by train, it was BR's fault in the 1960's for cutting the services down from Sheffield Victoria no wonder their was no passgengers.
Alternatively they were pragmatic. On the one hand they had a lightly used route that would require significant chunks of money to maintain even though there was little traffic, on the other they had a second route which provided sufficient capacity for all Sheffield - Manchester traffic. The sensible decision using the information to hand was to close the Woodhead as surplus to requirements.
As for passenger traffic those services were withdrawn at a time when the railways were seemingly in terminal decline. You would have been laughed out of the building if you'd suggested in forty years the railway would be carrying more passengers than at any time since before the Second World War.
You need to try and get over the loss of Sheffield Victoria and the Woodhead. They were surplus to requirement then and they were still surplus to requirement until very recently when it's possible that they might have been useful.
As for converting the 1500dc system to 25kv AC, their was talk about doing this around 1959/1960, they put it down to cost yet part of the line from Manchester to Hadfield/Glossop was done in 1984.
There is a huge difference between rewiring fourteen miles of heavily used commuter services and rewiring dozens of miles of lightly used mainline! I mean how can you not see that?
But getting back to the original thrust of this argument you've yet to demonstrate why closing the Woodhead was worse than all of the other Beeching Report closures, which was your original contention.