Initially, Bush demanded they take the city, and the commanders on the scene resisted. They thought a policy of "attrition" would soften up the enemy---right or wrong, it was their initial call. Not long afterward, both the Brits and the Iraqi interim government said they would not support a full frontal assault---the Iraqis, because they said their government would fall apart. Bush THEN instructed Sanchez to hold up.
The Marines transferred out within, as I recall, a month, and the Airborne came in. They maintained the cordon policy, then, a couple of months later, the Marines rotated back in. For those months, both military forces used the "attrition" strategy favored by the Marines the first time around.
West is NOT clear on whether this was the best approach. He concedes that the "attrition" likely saved hundreds of Marines, and probably kept the coalition together, not to mention keeping the Iraqi government in place. Nevertheless, at the same time, he seems to favor the "scorched earth" policy.
If you read "No True Glory," and come to a different conclusion, please let me know.