I think there is more to it than that.
We have had situations with no overground trains and only Southern trains before (possibly when there have been 4 trains per hour). Easter Sunday is one of the quietest days on the network, since all shops and businesses are closed, so shy the need for such an unusual arrangement?
But it became a tiny bit clearer at the end of last year in Lewisham Council's Transport Liaison Committee, in response to a question from the Forest Hill Society rep, that TfL are considering running services to London Bridge.
Since Southern now only run trains on the Sydenham corridor from West Croydon or Victoria, all services are within the GLA and it may be appropriate to shift the service to Overground. But this will inevitably become a political decision, so don't expect any changes before a general election.
But this alternative service will help to address any concerns about a possible switch and a new TOC terminating at London Bridge on a more permanent basis. Then we just need to persuade TfL to extend Overground from London Bridge through to Kings Cross, to fill the gaps on the Thameslink services.
In the meantime, it is important to keep reminding Southern, TfL, Lewisham, etc that the half-hourly service is not appropriate for the Sydenham corridor route to London Bridge.