Come on! 10 miles of single trolley wire and on a slow-speed line it probably won't wear out for decades.
It'll still wear out though. And it needs to be inspected regularly because if it does get in the wrong place, it'll cost a lot to put right. I suspect it'll not be able to do a simple trolley wire system because it's a twisty line with a number of quite exposed points. An urban tramway sheltered by buildings it is not. The wires will need to be able to stand up to a winter storm as well, increasing costs.
The idea that you could just plonk a few reclaimed telegraph poles down and run a single wire is wildly oversimplifying things. It wouldn't be a full GWML level project by any means, but it'll be more than something you could source from B&Q.
The battery charger will also require regular inspection, but that means inspecting 1 asset in a single location, not c.10 miles of OLE. You'd also be able to inspect the charger without needing to stop trains running, which would be harder (though not impossible) with OLE. The Train-board systems will also need inspection, but that'd be done at the depot and it's arguably easier to inspect a battery underneath a train than a pantograph on top of it.
The original wires were stripped out of the Woodhead route when it was closed and I have a feeling that some might still be in use (with new insulators) on the Glossop line
And when the train's traction batteries reach the end of that life, they can be repurposed for the trickle-charger, or other lineside batteries, and when they've finished that, they can be sold on to domestic applications. ALL systems require some element of renewal and maintenance, so let's not pretend that batteries are somehow unusual in needing to be renewed at end of life. The differences are in scale - an OLE system would need actual renewal every 40-50 years (as shown by the thread origin) whereas a battery system is likely to need replacing about every 8-10 years (according to the people running the Greenford shuttle in a recent interview).