I actually live in pretty much the same area and I'd say it's very well connected. If by a 'big night out' you mean in Central or West London, the tubes are extremely well connected with the night tube now running at weekends, so I've never had a problem getting home - 30 ish minutes, 40 tops if I have to take a slightly longer route because tubes lines aren't running or whatever. She will have the Victoria line (very well connected), Northern line and Clapham and Balham Rail services at her disposal. And for general nights out, South West London has heaps of good bars and clubs, so I definitely wouldn't say this is too far out!
Of course, she might also choose to uber everywhere. But personally, I love the nightlife scene here