Nothing was strange about DC overheads at the time, but to have a single line with DC and the rest of the network using AC, which would be the situation if Woodhead wasn't closed, would just mean that through freights and passengers would use diesel haulage. It would need an expensive conversion to function as an asset to the railway network.
The Altrincham line from Manchester was also 1.5kV DC from 1931 until it was converted to 25kV AC in 1971 (and then back to 750V DC for Metrolink in 1992).
The surviving Hadfield/Glossop section (12 miles) was converted to 25kV AC in 1984.
The remaining 28 miles to Sheffield would have been fairly simple to convert, unless new power supplies were needed.
But there would have been big network problems at the Sheffield end with onward connections.
The Penistone-Wath freight section would not have survived anyway.