This is a common question in so-called clear cut accidents. Often, this question is driven by a suspicion that the victim will simply end up with less money because the lawyer will take a portion of the recovery to cover his fee.
At the root of this suspicion is the assumption that the lawyer will not be able to substantially raise the amount of the recovery. However, our experience has shown that most victims simply do not have the expertise or experience to secure the full recovery to which they are entitled, even taking into account any reduction in the recovery to account for attorney's fees and costs. This suspicion is often subtly encouraged by the insurance adjuster assigned to the claim. There are even cases where adjusters have been know to affirmatively pressure victims into avoiding seeking assistance from counsel (e.g. If you want to hire a lawyer that's okay, but I'll have to reassign the claim to my supervisor, who is much more difficult to deal with.).
While it is certainly possible to handle your own claim, the relevant question is whether you are truly competent to do so. Frequently, the initial cooperation and attentiveness of the adjuster lulls a victim into a false sense of security. Remember, though, that insurance adjusters handle personal injury claims for a living, and that they have a natural advantage over untrained victims. You deserve a level playing field so that you can fairly compete with a trained adjuster who is working to minimize your recovery.