Evidence instead of assurance
A manufacturer can design excellent redundancy, thoughtful fail-safe behavior, and a well-reasoned risk assessment, and still have no way to prove any of it to an outside party. Certification is the structured, independent process that closes that gap. Instead of a robot maker simply asserting 'this system is safe,' certification requires producing documented evidence: records of the hazard analysis performed, the reasoning behind the integrity level assigned to each safety function, the test results demonstrating that redundant channels actually behave independently, and the failure analysis showing what happens under each considered fault condition. An independent body reviews that evidence against a defined standard and confirms, or refuses to confirm, that the claims are actually backed up.
This independence is the entire point. A manufacturer grading its own homework has an obvious incentive to be generous with itself, even unintentionally, since the people closest to a design are often the worst positioned to spot its blind spots. Bringing in an outside reviewer who has no stake in the product shipping on time, and whose job is specifically to find gaps in the safety case, produces a much more trustworthy result than internal sign-off alone. Certification doesn't design the safety measures, it verifies that the measures which were designed actually hold up under scrutiny.