Actually, on reflection, I suppose my Brentwood-Lewisham example is not that perverse. After all, going via the DLR is more convenient than via Southeastern.
The DLR option involves very regular service and fewer interchanges: Brentwood–>Stratford on EL or EL+GA (if doubling-back via Shenfield or changing at Romford to get a faster GA service); then Stratford–>Lewisham on DLR or LU+DLR (if going to Canary Wharf on the Jubilee line before changing to Canary Wharf DLR or Heron Quays DLR).
Conversely, the Southeastern option is more convoluted, and one leg relies either on a non-trivial OSI (New Cross Gate–>New Cross) or a not-so-regular LO service (4 trains per hour): Brentwood–>Stratford on EL or EL+GA; then Stratford–>Canada Water on LU; then Canada Water–>New Cross (only 4 trains per hour!) or –>New Cross Gate (8 trains per hour) on LO; then (having made the OSI from New Cross Gate to New Cross if applicable, which is a 7-minute walk in my experience) New Cross to Lewisham on SE.
Of course, once EL has through-running between the north-east branch and Paddington (due next month), the Southeastern option will get a bit simpler, since you will then be able to make a direct Brentwood–>Whitechapel journey on EL and change to LO at Whitechapel (instead of Canada Water). This could result in one fewer interchange (I say “could” because if doing EL+GA for Brentwood–>Stratford this would be cancelled-out by the extra interchange to return to EL for Stratford–>Whitechapel), and cut any need for the Jubilee line, although the gain is likely to be limited, since the Jubilee line is very regular and the LU-LO interchange at Canada Water (less than 30 seconds if you get the right carriage) is quicker than the EL-LO interchange at Whitechapel (minimum 2 minutes, I would say).
Glossary: DLR=Docklands Light Railway; EL=Elizabeth Line; GA=Greater Anglia; LO=London Overground; LU=London Underground; OSI=Out-of-Station Interchange; SE=Southeastern.