While Level 3, as currently implemented by some APIs, is a cargo-culted version of Fielding's idea of HATEOAS, Level 1 and 2 of the model have some usefulness for some types of APIs.
What you get by implementing what is called a "RESTful API" nowadays is something that is very different from the original concept of REST, but is still useful to some applications, over plain RPC.
Let's unpack it. Fielding RESTful system as a system which implement the following constraints:
1. Follows a Client-Server model
2. Is Stateless (request-response model)
3. Indicates cacheability of responses
4. Has Uniform Interface defined by the following restrictions:
Identification of resources (URIs); Manipulation of resources through representations (media types); Self-descriptive messages; Hypermedia as the engine of application state (HATEOAS)
5. Isolates access to non-adjacent layers
6. (Optional) Supports code on demand.
Applying all the restrictions stated above, lets you immense benefits: for instance cacheability, stateless and uniform resource identification make your system easy to distribute and scale to handle large amount of traffic; self-describing messages, manipulation of resources through representations and code-on-demand let you have a system that can evolve gracefully without requiring a big bang protocol upgrade.
The half-assed "RESTful APIs" of today implement only a subset of the constraints listed above. They are always client-serves, stateless, isolate access to non-adjacent layers and implement two of the uniform interface restrictions (URIs and manipulation of resources through representations). Sometimes they also indicate cacheability. However, they do not support HATEOAS (including most of the level 3 wannabes), code-on-demand and most importantly self-describing messages.
The lack of the constraints above means our modern APIs cannot achieve some of the benefits the web browser does: most notably flexibility and open-ended evolution. But they do have some other benefits over traditional RPC systems.
I think the maturity model itself is quite useless, but the following properties are useful:
1. Correct HTTP verbs: Differentiating between PUT and POST will let your intermediaries know when the request can be retried.
2. URIs uniquely identify resources: beyond the obvious benefit (cachability), it allows for easy sharding, distribution and smart redirection by any intermediary server.
With traditional HTTP-RPC (even with a standardized protocol like gRPC or SOAP), your intermediary has to be fully aware of the RPC schema to cache or know when it can retry. If you want to add a sharding gateway you need to especially develop a customized solution. A Level 2 "RESTful API" still has all these benefits.