Although there is a type of peer review that includes redoing experiments and analysis: artifact evaluation. All of the top conferences in my field (real-time embedded systems) include this as an opt-in option, and papers get a special badge if they also pass artifact evaluation. I strongly believe that other fields in computer science would benefit by including and normalizing this process.

Besides the reproducibility benefits, artifact evaluation forces documentation of the experiments and process; I've found this enormously useful when on-boarding new students to an existing project.