I think US energy independence is about as important as banana independence or iPhone independence, but others place greater import on it.
The DoE released its Annual Energy Outlook 2015 today and estimates in its reference case scenario energy independence between 2025 and 2030. If energy independence is a worthy goal the DoE shows some scenarios where the US can achieve that faster and even become a next exporter:
1) Low Economic Growth
2) High Oil Price
3) High Oil and Gas Resource
Which is one of the reasons I place little import on energy independence: The US can achieve that goal by suffering through low economic growth, high oil prices and high usage. How does that help?