U.S. playing "musical chairs" by shifting troops in Iraq to Baghdad

I found this off The Washington Post:

President Bush said today the U.S. military will move troops to Baghdad from other parts of Iraq in an effort to quell the rising sectarian violence in the Iraqi capital.

"The violence in Baghdad is still terrible, and therefore there needs to be more troops," Bush said at a White House news conference with Iraqi Prime Minister Nouri al-Maliki, who is on his first visit to the United States since becoming prime minister.

Bush said the unknown number of troops would be deployed in the "coming weeks." He said Maliki had recommended adding more U.S. troops alongside Iraqi troops in the violence-wracked Iraqi capital and "we're going to do that."

Bush said the deployment of additional troops in Baghdad "will better reflect current conditions on the ground in Iraq."

The current level of violence has shown few signs of decreasing and has eroded support for the war in both the United States and Iraq. Two men were gunned down inside their car in Baghdad today, news agencies reported, and the bodies of six people were found shot dead in different districts of the capital.

An estimated 100 people a day are being killed in Baghdad. The crimes, attributed largely to sectarian death squads, go largely unsolved.

"There need to be more forces inside Baghdad who are willing to hold people to account," Bush said.

So the president is going to pull U.S. troops out from other parts of Iraq to bolster the forces currently in Baghdad, which has been facing a high level of violence. I have a question for you Mr. President. If you pull troops out from other parts of Iraq to stem the violence that is wreaking Baghdad, then those other parts of Iraq will have a decreasing level of security due to the decreased number of troops stationed in those other parts of Iraq. The Iraqi insurgents will certainly recognize that, and may just start increasing the level of violence in those other parts of Iraq that have sent troops to Baghdad. How will the U.S. military respond to this possible adaptation? You may end up stemming the violence in Baghdad, but at the expense of increasing the level of violence in the other parts of Iraq.

Have you considered this scenario Mr. President?