The Model Registry is mostly a workflow tool. It helps 'gate' the process, so that (for example) only authorized users can set a model to be the newest Production version of a model - that's not something just anyone should be able to do!
The Registry can trigger webhooks when a model enters a new state, for example to run a testing notebook when a new Staging candidate appears.
It also helps serve as a single source of truth: what's the current production model? rather than pass around the run ID "abc123456..." informally, the stage tags in the Registry let any process look up the 'latest production model' reliably.