Are there side effects to Postgres 12's NOT MATERIALIZED directive?
It's explained very well in the documentation.


  A useful property of WITH queries is that they are normally evaluated
  only once per execution of the parent query, even if they are referred
  to more than once by the parent query or sibling WITH queries. Thus,
  expensive calculations that are needed in multiple places can be
  placed within a WITH query to avoid redundant work. Another possible
  application is to prevent unwanted multiple evaluations of functions
  with side-effects.


So far, so good, BUT:


  However, the other side of this coin is that the optimizer is not able
  to push restrictions from the parent query down into a
  multiply-referenced WITH query, since that might affect all uses of
  the WITH query's output when it should affect only one. The
  multiply-referenced WITH query will be evaluated as written, without
  suppression of rows that the parent query might discard afterwards.


So, as pointed out in the example given, if you have a query like this:

WITH w AS (
    SELECT * FROM big_table  -- big_table has an INDEX on a field called key!
)
SELECT * FROM w AS w1 
  JOIN w AS w2 ON w1.key = w2.ref  -- w is called TWICE, so DEFAULT is MATERIALIZED
                                   -- PostgreSQL can't take advantage of big_table.key
WHERE w2.key = 123;


So, in this case:


  the WITH query will be materialized, producing a temporary copy of big_table that is > then joined with itself — without benefit of any index


Far better to have:

WITH w AS NOT MATERIALIZED (
    SELECT * FROM big_table
)
SELECT * FROM w AS w1 JOIN w AS w2 ON w1.key = w2.ref
WHERE w2.key = 123;


So that the optimizer can "fold" the CTE query "into" the main query and make use of the INDEX on the key field of big_table!

Re. the DEFAULT of NOT MATERIALIZED:


  However, if a WITH query is non-recursive and side-effect-free (that
  is, it is a SELECT containing no volatile functions) then it can be
  folded into the parent query, allowing joint optimization of the two
  query levels. By default, this happens if the parent query references
  the WITH query just once, but not if it references the WITH query more
  than once.


So the DEFAULT is NOT MATERIALIZED if: 

    the_query IS NOT recursive 
AND the_query is_side_effect_free 
AND the_query is_run_only_once


otherwise you have to tell PostgreSQL to use NOT MATERIALIZED.   

The only small problem that I see is that testing will be required to see if 
NOT MATERIALIZED is an improvement or not? I can see circumstances where the balance will swing between the two depending on table size, fields selected and indexes on the fields and tables used in the CTE - in other words, there's no substitute for knowledge and experience. The DBA isn't dead and gone yet! :-)