An extension of the Northern Line on a new trajectory from Kennington via Brixton to Streatham, with the majority of trains in the peaks running via Bank, would have been a far better way of getting the tube into this area imo, combined with the existing Victoria Line of course. If we weren't talking GB then a modern tram system from West Croydon as far as Kennington at least would be not only feasible, but desirable, but we're utterly incapable apparently of translating this to reality any more.
The reality of Kennington, surely, is that unless the whole lot of tracks and tunnels there were rebuilt (so closing the southern half of the northern Line for goodness knows how long), it was always only feasible to add any new southern extension in a way that linked it exclusively to the Charing Cross branch.
Remember that the anywhere-to-anywhere-without-conflicting-movements set up at Camden Town was built
at the time when the second central London route was added to the mix there. And of course people complain that having all combinations operating cuts capacity at busy times compared to if there were through routes with no routine junction movements.
If the aim is to have an extra southern terminus of the line, with most - at least - trains from one terminus using one central London route, then the new route using
exclusively Charing Cross and most Mordens going via Bank is the only feasible option. From a passenger perspective, there are of course arguments in favour of an anywhere-to-anywhere set-up like at Camden Town, but it wasn't on the cards for Kennington - having
any of the new route going via Bank, let alone most - as suggested above - was a non-starter.
Of course, irrespective of this, if the direction of the new route had been chosen on the basis of the needs of existing Londoners, rather than according to the bribes of property developers, it would certainly have gone on one of the trajectories mentioned in this thread, and not to Battersea.