The purpose behind statutes of limitations is to ensure that the legal system is fair. When too much time passes, there could be a lack of evidence necessary to disprove the claim against the defendant. Because the burden of proof is lower in civil cases, it’s important to make the process as fair as possible.
Also, an accident victim with a legitimate claim should presumably pursue their case with reasonable diligence if their damages were significant. Waiting beyond the statute of limitations to file a claim means the claim wasn’t a valid cause of action.