The following might be a little too vague for what you want.

The "generalization/specialization" pattern,  like many tools and techniques
in information science, is not strictly necessary.  It is possible to model
Doctors and patients without ever making explicit the fact that they are
both "people".  Just about everything you need to do with the data can still
be done.

In such a model,  if a curcumstance were to arise where a given person were
both a doctor and a patient in the same database,  the fact that a givven
SSN might identify a doctor in one context,  and a patient in another
context,  would be "obvious"  to the people working with the data with an
understanding of the subject matter.  It would be pretty opaque to the
people working with the data, but with no understanding of the subject
matter.  That might or might not be ok.

As to whether generalizations are useful or not,  that's another story.
There are many situations where realizing, for instance, that autos and
trucks  (lorries?)  are both "vehicles" can help the database designer,  the
programmer,  the interactive user,  and the user of reports or other
extracts.  It makes things easier, in a lot of situations.  Having said
that,  I'm quick to add that it's not the silver bullet of data modeling.

The way I learned modeling (which might not be the most usual way) gen-spec
is used for modeling at the ERD level.  That is,  it forms part of the
conceptual data model.  The question might arise about what happens when one
designs a relational schema to conform to the conceptual model,  when the
conceptual model contans a gen-spec pattern.

As you stated,  the most mechanical transformation of ERD into relational
schema will result in an extra relation for the generalization.  The
question might be asked,  "is this good design or bad design?"  I think this
is what you are really asking.  My answer is,  "it depends".

And I would suggest that the purely mechanical transformation from ERD to
relational schema masks the fact that some real design work is going on when
this transformation is done.  The fact that you can do it without thinking
doesn't mean that you should do it without thinking.  It seems to me that in
some situations,  the "extra" relation is worth its cost.  In others, it
isn't.  You will undoubtedly get other insights from other people regarding
this.

Not that,  if someone is exposed only to the relational schema,  it might
take a little deduction on that person's part to discover that the relations
were intended to mimic a gen-spec pattern.
Deducing design intent from implementation is another whole discipline in
the general field of information systems.