If the only means of recompense for an employee who is injured on the job is to sue his employer, this puts an injured employee in the awkward position of having to sue his employer; if the employee is subsequently dismissed for whatever reason, it may put the employer in the awkward position of having to show that the dismissal was not a form of retaliation for the lawsuit.
In theory, workman's compensation avoids the conflict by creating a system where employees have no disincentive to seeking to have their injury-related costs paid, and employers are not seen as having any basis for retaliation. Such a system is not without advantages. The problem is one common to many types of insurance--its existence can alter people's behavior, and can very easily create feedback loops which can cause costs to spiral out of control especially if an insured party can profitably engage in behavior which substantially increases the likelihood of a claim, but the costs to the insurer will be sufficiently diluted among other insured parties that the profit from the behavior exceeds the portion of the costs paid by the person engaging in it.
And faster as well. Perfectly good workers are patched up quickly and put back on the job.