Technically, yes, and I agree with your premise. Here's where that ship has run aground, though.
The idea behind the Army transformation is to create a light, mobile, lethal force. One that will tear apart other conventional military forces fast, accurately, and with minimal casualties. Even in it's semi-transformed state, that's what we saw in 2003 against Saddam's army. The Pentagon wants a force that can do that against anyone. Like, say, China.
Having a large mass of light fighters, against their large mass of light fighters, runs the risk of high casualties. That's why the brass, increasingly gunshy of the media, is averse to the idea.
What we're starting to see is that the enemy doesn't have to lie down and play dead, just because Force XXI shot all of it's tanks from 2 miles away. Our light, lethal, agile force is death incarnate against enemy armor, but it isn't heavy enough to occupy and enforce our will on a resisting populace. That takes boots, and lots of them.
So, cost savings aside, we need more ground pounders, especially of the SOF variety. Not peacekeepers, not warfighters, but surgical instruments of U.S. power. People who can actually accomplish United States foreign policy objectives once major combat operations stop, and the tough work of winning the peace starts.
We never want to lose the 'death incarnate' conventional power. It's the best thing our tax dollars go to, hands down. We just need to add useful components, like the light fighters you mention, to round out our capabilities. Spending three years losing what you won in three weeks is a hard thing to do. It didn't have to be this way.
Still I think we might have had a bigger impact on the war effort looking for stuff crossing the border from Iran or Syria. Scouts are taught a lot of counter-infiltration stuff too. OIF III was about 40% guard troops and I couldn't make much sense over how we were deployed, it seemed to me that a lot of units were just plugging holes without much consideration given to their respective strengths.
Bear in mind we have 400,000 some Iraqi soldiers, with arabic language skills and familiarity with local customs.
We should plan to complement and supplement, not supplant that force.