High voltage AC actually gives more overhead than the same voltage DC.

HVDC is enormously expensive even today and completely impractical for bulk transport 100 years ago. You can't look just at corona, capacitive etc. losses of HVAC, you need to factor in the entire economic equation. The total overhead of AC (cost of equipment + energy lost for the lifetime of the line) is still lower for overground transport over reasonable distances and will remain so for the foreseeable future.