This would be a very special case for COPY. It applies only to a single column of JSON values. The original problem can be solved with psql --tuples-only as David wrote earlier.
$ psql -tc 'select json_agg(row_to_json(t)) from (select * from public.tbl_json_test) t;'
[{"id":1,"t_test":"here's a \"string\""}]
Special-casing any encoding/escaping scheme leads to bugs and harder parsing.
