The extension prevents a more useful extension of the Northern line to the south, heading towards Streatham.
The line ends too early rather than joining with other rail arteries at Battersea Park or Clapham Junction.
If taking the proposed route there should be interchange capability at Oval. The lack of connections is a major flaw in the project and goes against all recent experience of rail projects in London (i.e. Jubilee, Crossrail, Thameslink, ELL1, ELL2)
The best way to connect Battersea to central London is the mainline train service out of Waterloo Eurostar, which sits empty and with spare capacity for suburban services. This would also provide interchange with the Victoria line at Vauxhall.
An over river monorail system from Battersea to Embankment would be cheaper and provide more additional capacity than the proposed extension.
Wandsworth Road station would need to be renamed if the Nine Elms station is built on the same road.
If you want to build a new tunnel in South London there are much better options available, including the Northern line to Streatham and the Bakerloo line to Lewisham/Bromley.