I work for a company that averages around 50 production deployments per day for our customer-facing ERP, and we only do code reviews for new devs and changes to underlying framework changes for mostly the same reason sklivvz1971 mentions. We rollback very infrequently and a majority of our devs can deploy to prod with the push of a button as needed (this includes both application and database code). Not arguing that code review is unnecessary, just feel that with proper training and having devs with good judgement can help reduce the likely hood of breaking things when deploying small changes frequently.
We rarely catch things breaking in code reviews, I agree they are really bad at finding bugs. Automated tests and linters are better at finding stuff like that. The things we usually address in code reviews are architecture and code design issues, and occasionally edge and interaction issues that are outside the scope of what might have been considered when implementing.
We also have frequent production deployments that everyone on the team can do, I view that as something that is independent of code review.
