Why? The whole idea of comparative advantage is that you can increase your overall standard of living by making the things that you are best at and importing everything else. The only reason why you would want to be independent is if you planned on fighting a war with all the other countries in the world at the same time (granted, this could be the policy of our current US administration). Interdependence creates peace.
If China attacks Taiwan, they will have the huge percentage of their GDP that consists of trade with the US on the line. So I consider outright military conflict unlikely. However, if we were as "independent" as you suggest I think war would be much more likely.
Why again is independence a good thing?
"Energy Independence" is probably a misnomer - but the point is to change our economics so that we aren't forced to provide advantage to our geostrategic adversaries. Because our economy is so dependent on oil, we currently have little choice but to fund those who currently fund our (the U.S. and the rest of the West) enemies. The desire is simply to make oil a commodity like any other, and not one that can make or break the U.S. In other words, we need something to give us the ability to tell the Saudis to kiss off.
And then we can invade the Saudis! Brilliant!
Realize I'm using "the Saudis" as a proxy here. But further:
Can you imagine a scenario in which the following things are true:
a) we buy, say, 40% less oil overall
b) we have the same tensions with SA and Iran as we do now
c) SA and Iran are as rich as they are now (translate: capable of financing terror groups to fight proxy wars) ?
I can't.
Having to create electricity to meet our energy demand is a fantastic problem to have. Energy independence should be an economic goal of any developed country. You don't want ANY foreign control of 7% of your GDP, let alone a cartel like OPEC.