The net cost is that of the transaction charges.
The net cost to the the railway / Network Rail. The net cost, in money and other less tangible costs, to the locality and the proprietors of the closure of a viable farming business[1], and at least one other business, plus a number of people being moved out of their homes, is not neutral.
I have a radical alternative suggestion: Network Rail, DfT at al could manage their crossings better and if they have to force the closure of crossings do so in a manner that minimises the impact on people outside the railway business rather than focusing on minimising the impact on the railway business.
In any case, any actions leading to the closure of this crossing will take time. In the meantime this crossing, and all the others, will need to be properly managed rather than (as Network Rail seem to have adopted, by default rather than design, as policy for a while), assuming they can be ignored as they will all be removed eventually, at some indeterminate time in the future.
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[1] Or rather, loss of use of a large proportion of it's fields for a period of time - the farm buildings are the other side of the road from the turning to the LC. Which is as good as closure, since sheep cannot just be packed away in a warehouse for a while - they need to graze somewhere and spare pasture isn't just lying around idle, for the taking. Neither can flocks just reestablished from nothing.