That was definitely the thinking of NeoCons from 2001-2005/6, after the quick victory General Tommy Franks delivered in Afghanistan over the Taliban. Just as he was getting ready to wrap up the first year of the war in Afghanistan, Rumsfeld told him to start preparing plans for Iraq.
His successive quick victory of Iraq over Saddam in April/May 2003 furthered entrenched this thinking. Moreover, as the Iraq War dragged from 2004-2005 with no end in sight despite serious battles in Falluja (Fall 04) and Najaf, this type of thinking was used as a justification for continuing the un-decisive war in Iraq. (Remember that at this time Afghanistan was rather chill... It didn't start to lighten up until 2008. For most Afghanistan was a done deal)
This type of thinking, however became challenged in 2006 with the beginning and in fast escalation of ethnic killings in Iraq. Instigated by Zarqawi's Al-Qaida in Iraq when his suicide bombers blew up the Shia Al-Askari Mosque in Samarra, Iraq. It became evident that violence in Iraq could not be contained by simply having US soldiers in bases around the country, and there was a risk of the country being fractured. And with that chaos came the threat of entry of Iraq and Saudi influence into Iraq as those two regional powers competed to pick up the pieces of the mess.
Two pivotal events in 2006/2007 changed Iraq's security for the better. #1 The Anbar Awakening by Sunni insurgents who got fed up with Al-Qaida in Iraq and asked for a partnership with the US forces. From here on we get to Sons of Iraq. #2 General Petraeus, General Odierno, and others, and the surge.
From 2007 onward that line of thinking the OP has posted has been on the decline.
As for Afghanistan...... what we are currently seeing is what happens when after nearly destroying the Taliban in 2001/02 the US did two BIG mistakes:
(a)It send the bulk of its forces, and focused the attention of the DOD in Iraq.
(b)It left Afghanistan AS IT WAS in 2002.
The result is that the Taliban regrouped, re-organized, found new ways of funding their operations, new leaders emerged, and consolidated their position in Pakistan. THEN, about 6 years later the Taliban return to the offensive in Afghanistan.
And the US responds with Genera McChrystal, 30,000 more troops, and a "new" strategy. However, McChrystal was not making progress due to relying on the National Afghan Army/Police. He then fucked himself up with the Rolling Stones article. Now General Patreus was demoted from head of CENTCOM, to head of forces in Afghanistan to win the thing.
...and that's how we ended up here.
Now among members of the Military and State Dept a consensus is building in the knowledge that the Number ONE Cause of our security threats in the Middle East is:
The harsh Israeli occupation of the West Bank, and settlement building in the West Bank.
Other causes are the corruption and authoritative gov'ts, and the poverty in which the majority of the population lives in. In this poverty, extreme Islamic groups provide basic welfare services to win the sympathy of the poor folk. The Islamic groups then use the Israeli occupation, US wars in Iraq and Afghanistan as propaganda to recruit new men, AND have the wealthy/elite members of society give them $$.
.........THAT is what is going on right now fellas.