Easiest way to eliminate NULLs in SELECT DISTINCT?

Try this:

select distinct * from test
where b is not null or a in (
  select a from test
  group by a
  having max(b) is null)

You can get the fiddle here.

Note if you can only have one non-null value in b, this can be simplified to:

select a, max(b) from test
group by a