...Broadly Network Rail want to try and "four track" the railway between Northallerton and Newcastle by using alternative routes. With the alternatives becoming the "slow" lines for the ECML and the passenger traffic remaining concentrated via Durham. It's why their route utilisation study (or whatever it was called) wanted to explore re-opening, at least in part, the Leamside line...
I can't see what part of the Leamside line could be reopened bearing in mind that it is only at the two extremities (i.e. Pelaw and Ferryhill) that it connects with existing track.
Apart from the not inconsiderable task of clearing the vegetation (and detritus) that has sprung up along it, there appears to be at least one large (and presumably expensive) issue with reopening it, at Washington. The A1290 (the link road from the A19 past Nissan to Washington, crosses the old formation on the level with a couple of roundabouts pretty close by. A road bridge would need to be built (I assume a new level crossing would be frowned on) with maybe at least one of the roundabouts moved (or removed).
There are also "level crossings" at Follingsby Lane between Washington and Pelaw, and Fencehouses which would need to be dealt with. All other road crossings appear to be under- and over-bridges which would need fettling. The formation is also in a worse state than the Bicester to Bletchley line was. So it's perhaps not quite as cheap as initially appears (but still cheaper than alternatives)
Of course, should the Metro extension from South Hylton, across the Victoria Bridge, through Washington and north to Pelaw ever come to fruition, then interaction with a heavily used freight corridor would be interesting. (This situation is catered for already on the Sunderland to Pelaw line which is used by Grand Central, Northern, Freight and Metro - uniquely perhaps in the UK - so it can be done, although the freight traffic is not perhaps as heavy there as would be on a reopened Leamside line).