Every once in a while I get this requirement, not often for documents, but often enough for sites that the solution applies to items, documents, sites and external content not stored in SharePoint. The solution is to create "excerpts" or "linked items" that contain enough information about the documents in question that users can search for the links and then request access to the associated content.
Yes, it does require more work, but this work can be automated. For example a Flow could be created that extracts the opening paragraph, or the summary section, of the document and create a list item in a "public" list that the users do have read access to. You could even have the Flow copy the metadata along with it to improve findability (you are using metadata...right?). SPO will index the items and provide the results to your users. We have further augmented the Display Template to include a link to "Request Access" where the user completes a request form and then another flow runs to process the approval request, ultimately adding the requesting user to the readers group on the library.
I wouldn't say its "Impossible" it just requires an understanding of how the pieces fit together so you can create a solution to your business problem.