Battery bi modes are cheaper to maintain than DMU's and much lower fuel costs.
Don't forget the cost of maintaining the OHLE once installed which will be much higher than any slight increase in maintenance costs from having to maintain the batteries.
Don't forget that most battery trains are no heavier than the diesel alternatives.
Traffic levels are low in terms of TPH and also passenger capacity per hour.
Don't forget that the line is single track, so for an hourly service each way, you get two trains an hour on the infrastructure. That's not much different from many electrified routes.
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How many bridges need rebuilding that is not cheap
From the overhead bridges I can remember, most seem to be arched bridges for double track, so plenty of room in the middle for single track OLE.