If the x-rays taken do not reveal any serious injuries and they confirm that you only have soft tissue injuries (i.e. contusions), then you will have piece of mind knowing that you didn't suffer any serious injuries that would require extensive treatment or surgery in the future.
One common mistake that people who are involved in accidents make is not getting x-rays done as soon as possible, because they hope that their neck or back pain will just go away. However, months or even a year or more later when they are still in pain, equal or worse to the pain they felt shortly after the accident, they finally decide to get x-rays done. If the x-rays or MRI reveal bulging or herniated discs or other serious back/neck injury, the insurance company will have a legitimate argument that during all those many months between the accident and the date when those x-rays were taken a lot of things could have happened to you that caused or aggravated the injury shown on the x-ray image. After all, if the injury was caused by the accident and it is as bad as you claim it to be, why didn't you get your x-rays done back then, on the day of the accident or shortly after. It is particularly hard to explain why you didn't get x-rays done, if you reported to the emergency room right after the accident, where getting x-rays is usually a standard procedure.
Although the above arguments by the insurance companies and their lawyers are not always effective, especially if there is no evidence of subsequent injuries, it still gives them yet another weapon to argue that you shouldn't be compensated as much as you claim you should.