REST for nested paragraphs
No. Core REST &amp; REST Views aren't the right solution here. You don't need a custom module for this.

As you mentioned, JSON API module supports inclusion of entity references in a single resource request. Each entity requested has a property called relationships which are references to other entities that can be included with via the include parameter. References, within references (e.g. a node referencing a media entity, that references a file entity) are supported too, albeit with some work to follow references (e.g. when you a request inclusion via the include property you're given an array property, included, which you still have to sort through via id).

If you're looking for a Drupal API that follows entity references within returned entity objects, you should use the GraphQL module as it will allow you to define your own data spec that can expand entity references as you see fit.