At least in PostgreSQL, both by alias and ordinal are possible:

  localhost(from SCB-MUSE-BOXX).postgres.scb.5432 [Sun Nov 16 12:02:15 PST 2025]
  > create table test (a_key integer primary key, a_group integer, a_val numeric);
  CREATE TABLE
  Time: 3.102 ms

  localhost(from SCB-MUSE-BOXX).postgres.scb.5432 [Sun Nov 16 12:02:25 PST 2025]
  > insert into test (a_key, a_group, a_val) values (1, 1, 5.5), (2, 1, 2.6), (3, 2, 1.1), (4, 2, 6.5);
  INSERT 0 4
  Time: 2.302 ms

  localhost(from SCB-MUSE-BOXX).postgres.scb.5432 [Sun Nov 16 12:02:58 PST 2025]
  > select a_group AS my_group, sum(a_val) from test group by my_group;
   my_group | sum
  ----------+-----
          2 | 7.6
          1 | 8.1
  (2 rows)
  
  Time: 4.124 ms
  localhost(from SCB-MUSE-BOXX).postgres.scb.5432 [Sun Nov 16 12:03:15 PST 2025]
  > select a_group AS my_group, sum(a_val) from test group by 1;
   my_group | sum
  ----------+-----
          2 | 7.6
          1 | 8.1
  (2 rows)
  
  Time: 0.360 ms

The problem with this and similar requests is that it would change the identifier scoping in incompatible ways and therefore potentially break a lot of existing SQL code.

I think it should be not only in GROUP BY, but in every context, e.g., inside expressions in SELECT, WHERE, etc.

PostgreSQL and DuckDB support this, which makes MSSQL feel like a dinosaur in context.

Some do. It would also be nice to reference by ordinal number similar to order by. Very handy for quick and dirty queries. I can see the issue though that people start to lean on it too much.