If you're referring to Router from compose-router, I can comment on why I think it's useful, but your mileage may vary.
For one, It allows you to stay completely in Compose world. You don't need more than a single Activity as an entry point. You don't need Fragments. In a sense, this makes your tech stack thinner, and you can avoid some misery with Intents, flags, obscure back stack operations, transactions, and a lot of things you otherwise can only learn the hard way.
With a Router approach, back stack is just a list of simple objects, and you can easily write your own list operations. Boom, done. Plus you can pass data directly between layers with full compile-time safety, no need for Intents.
Also, with a Router you can represent logical state switching (logged out / logged in), screen switching, sub-screen switching (view pager) with the same lightweight pattern. Again, fewer things to learn the quirks of, and a simple and universal tool / pattern to achieve more things.
Local navigation: this is a huge benefit if you have any kind of shared modules between multiple apps. And even if you don't, it's a much simpler solution to navigation problems. With a top-level Navigator approach you run into the issue that Navigator has application-specific navigation operations. But a shared module cannot know anything about those, because they may vary between different apps. You can approach it from the other side, and it's still bad: instead of defining what navigation operations you offer, you could satisfy the navigation dependencies of the shared modules by some top-level wiring. This requires constant maintenance, and works only as long as you reuse shared modules 1 level deep. Any module deeper down could change as an implementation detail of the level above, and now the top-level app is broken. Contrary to this, a Router approach allows you to implement navigation as a local concern of the module you are writing. All the above issues are boom, gone.
Granularity: Activities mean a full screen. Fragments can mean smaller parts, but I haven't really seen an example of leveraging this down to the level of what's achievable with Compose. With Compose you could introduce a Router at any level in the tree, helping you to organise it in much thinner layers.
Downside: you probably don't want to go full Compose on an existing, large codebase, as it's almost equivalent to rewriting it from scratch. But if I'd start a new app today imagining that Compose is production ready, I'd not hesitate to leave Activities, Fragments far behind, and go full Compose.