As I mentioned in post #31, the Overground does have a high frequency ELL core.
In contrast, the Elizabeth line at Reading is a train every 30 min.
So in other words, both Overground and Elizabeth line have a high frequency core, with sparser services at the extremes.
There's no 'core' on any of the six Overground lines, in terms of London rail transport terms. 'Cores' are areas within central London area that serve major destinations with through services. Whitechapel to New Cross is no more central London than Kensington to Clapham Junction is. The London 'cores' are the Lizzie, Thameslink, both branches of the Northern line, Central, Piccadilly, Victoria, Jubilee & District Lines. Their services are justified by the very large numbers of footfalls at their stations around and within the circle line, and interchange traffic from other 'core' stations.
Arguably, the most intense part of the total Overground line network is the stretch between Dalston Kingsland/Junction and Highbury & Islington. None of this is denigrating the effectiveness of the Overground lines, they have been very successful in providing circumferential and some inner radial services on what was drifting towards derelict National Rail provision. AFAIK, local communities see them as essential local links.