They allow you to match the URL in a series of steps. Where each step can be static (ie "/foo") or dynamic (ie /images/).

You can then easily add features to this structure, like route middlewares at every level in the tree; just apply them while doing the routing.

This also allows you to match route variants easily, ie "foo" and "foo/" are the same, so are "/" and "/index.html". In the same way you can extract query parameters for middleware/handler use.

A trie is O(k), where k is the length of the key on inserts and deletes. Generally, any hashing algorithm is also O(k) with the additional overhead of the lookup in the table. This also ignores that most hashes have only amortized O(1) inserts. A trie usually also exhibits better memory locality and caching behavior. Also, a trie (like most tree data structures) can be implemented in a lock-free format fairly easily.

A hash map doesn't solve the same problem. Given a collection of routes, you need to find the longest one which is a prefix of the given URL.

A trie can efficiently match all routes that start with a prefix. With a hashmap you wouldn't be off any better than a list efficiency wise.

Fixed lookup time. A trie (aka radix tree) 3 levels deep with 1 million entries has the same lookup time as a 3 level deep trie with 5 entries.